It is unanimously accepted that the original word in the Hebrew Bible is 'Baca'. The context clearly indicates that it has been used as a proper noun and most of the versions and translations of the Bible have retained this status. Some of the translations and versions have misconceived its status and have taken it to be a common word. Then they tried to translate it whimsically as: weeping, tears, balsam tree, mulberry, some of the other trees, dry valley, etc. It does not seem to be a proper approach and is based on some misunderstanding.
The Hebrew word 'Baca' is composed of three alphabetical letters = בכא(b→k→a). According to the Strong's Dic. of the Heb. Bible it means:
'weeping' or 'the weeping tree (some gum-distilling tree, perhaps the balsam,):—mulberry tree.' . 'Bakah' is also composed of three alphabetical letters = בכה(b→k→h), meaning 'to weep; gen. to bemoan, to bewail, complain, mourn, with tears, weep'.
The vowel symbols had not been introduced in the Hebrew writing system until the seventh/eighth century AD.It was only after their introduction in the Qur'ān in the 7th century AD that some proper vocalization system for the Bible was developed somewhere in the beginning of the seventh century. Before the introduction of thevocalization system in Hebrew writing, the words 'Baca' and 'Bacca'; or the words 'Bakah' and 'Bakkah' were to be written in the same way. King David had actually and naturally used the word 'Bakkah' in his Psalm. Because the words 'Bakah' and 'Bakkah' were written in the Hebrew script in the same way, it got the pronunciation of 'Baca' or 'Bakah' instead of the correct pronunciation of 'Bakkah' in the later Jewish ages. This 'Bakkah' was the ancient name of 'Makkah' and was given to it by Abraham. Originally the city was called by this name. Here are some of the Arab authorities to elaborate it:
'Lisan al-'Arab' (the language of the 'Arabs), a renowned Arabic Dictionaryin 18 volumes, explains:
Ya'qub says, 'Bakkah is what is situated in between the two mountains of Makkah, because the people crushed one another during the circumambulation or overcrowded there. (…). It is said that Bakkah is the name of the interior of Makkah and it was given this name due to the crowding and swarming of the people. The tradition of Mujahid states, 'Bakkah is among the names of Makkah.' And it is said, 'Bakkah is the site of the House of the Lord, and Makkah is the whole of the city.' It is also said, 'Both [Makkah and Bakkah] are the names of the city; and [the alphabetical letters] "B" and "M" succeed (can replace) one another.'
Tahdhib al-Lughah (in 16 volumes) is one of the most reliable dictionaries of the 'Arabic language. It explains the word as follows:
Al-Layth says: al-bakk means breaking the neck. It is said that Makkah was named Bakkah because it broke the necks of oppressors when they deviated from the right course. And it is said that Bakkah was named Bakkah because the people crushed or pushed away one another in the paths. 'Amr reports from his father: Bakka something, i.e. tore or disjointed it; and from it was derived Bakkah, because it broke the necks of the oppressors and tyrants when they transgressed in it. It is also said that it was named Bakkah because people crushed one another in its routes. (…).
Zajjaj says: It is said that Bakkah is the site of the sanctuary, and what is all around it, is Makkah. He [Zajjaj] said: and there is consensus on it that Makkah and Bakkah are the place where the people resort for pilgrimage; and it is the city. And he [Zajjaj] said: And as far as its derivation in the lexicon is concerned it would be appropriate to say that 'the people crushed one another in the circumambulation, i.e. pushed away one another.' And it is said: Bakkah was given this name, because it crushed the necks of the tyrants.
'Mu'jam al-Wasit~' says, 'Bakkah = Makkah'.
'Bakkah' is the name of the inner portion of 'Makkah'. It was thus named because of the overcrowding of the people [in it]. It is also said that it was thus named because it crushed and broke the necks of the oppressors.
Tartib al-Qamus al-Muh~it~ has also explained 'Bakkah' in a fair detail:
'Bakkah' stands either for 'Makkah'; or for what lies between its two mountains; or for the field of circumambulation [Mat~af], because it crushes and breaks the necks of the arrogant or because of the overcrowding of the people in it.
Muh~it~ al-Muh~it~ is also one of the authorities of the 'Arabic lexicons. It is a revised and advanced version of Firuzabadi's renowned 'Qamus'. It has also recorded similar explanation of the word:
It is the name of what lies between the two mountains of Makkah or of the circumambulation field [Mat~af]. It is said that it was so named because it crushes and breaks the necks of the arrogant or because of the overcrowding of the people in it.
Mu'jam Maqayis al-Lughah is an authority as regards the basic roots of the Arabic words. It explains the word as follows:
'Al-Khalil' says 'Al-Bakku:crushing the neck', and it is said that 'Bakkah' was named so because it used to crush the necks of the oppressors. When they inclined towards oppression, they were erased from the scene. It is also said that it was named 'Bakkah' because the people crush one another during the circiumambulation or pushed them away.
Al-Khalīl bin Ah~mad (100-175 A.H.) is one of the greatest, if not the greatest, authorities on Arabic lexicon. The first Arabic lexicon, Kitāb al-'Ayn, was compiled by him. He explains:
Al-Bakku: to crush the neck. Makkah was named Bakkah because people crush one another in the T~awāf (circumambulation of Ka'bah), or push one another due to overcrowding. It is also said that it was so named because it crushed the necks of tyrants when they deviated (from the right path) in it by way of oppression.
'Akhbār Makkah' is a detailed history of 'Makkah' in six volumes in the Arabic language. Here are some excerpts from its section on 'Names of Makkah':
One of the residents of Makkah (…) gave me a book written by some of his forefathers. In it were stated the names of Makkah which the residents of Makkah claimed to be, i.e. Makkah, Bakkah, Barrah, Bassasah, Umm al-Qura, al-H~aram, al-Masjid al-H~aram, and al-Balad al-Amin. Some people say that 'S~alahi' is also among its names. Some of the Makkans claim that 'Kutha' is also one of its names.
It is written beneath 'al-Maqam', I am Allah, Lord of 'Bakkah'. I sanctified it on the day when the heavens and the earth were brought into existence.
The Qur'an has used both 'Makkah' and 'Bakkah' for the name of the place. When it is mentioned as a place of the ancient times it has been named as 'Bakkah', as it has been used in sūrah A^l 'Imran (3) of the Qur'ān:
إِنَّ أَوَّلَ بَيْتٍ وُضِعَ لِلنَّاسِ لَلَّذِي بِبَكَّةَ مُبَارَكًا وَهُدًى لِّلْعَالَمِينَ فِيهِ آيَاتٌ بَيِّـنَاتٌ مَّقَامُ إِبْرَاهِيمَ وَمَن دَخَلَهُ كَانَ آمِنًا وَلِلّهِ عَلَى النَّاسِ حِجُّ الْبَيْتِ مَنِ اسْتَطَاعَ إِلَيْهِ سَبِيلاً وَمَن كَفَرَ فَإِنَّ الله غَنِيٌّ عَنِ الْعَالَمِينَ 
The first House ever to be built (as sanctuary) for men was that atBakkah (Makkah), a blessed place, a beacon for the nations. In it, there are clear signs and the spot where Ibrahim stood. Whoever enters it is safe. Pilgrimage to the House is a duty to Allah for all who can make the journey.
There is another occasion in the Qur'an where it has been mentioned in the perspective of the period contemporary with the Prophet of Islam:
وَهُوَ الَّذِي كَفَّ أَيْدِيَهُمْ عَنكُمْ وَأَيْدِيَكُمْ عَنْهُم بِبَطْنِ مَكَّةَ مِن بَعْدِ أَنْ أَظْفَرَكُمْ عَلَيْهِمْ وَكَانَ اللَّهُ بِمَا تَعْمَلُونَ بَصِيرًا
It was He who restrained their hands from you and your hands from them in the valley of Makkah after He had given you victory over them. Allah was watching over all your actions.
Here it has been mentioned with the name of 'Makkah', which shows that in the times of the Prophet of Islam the city was named as 'Makkah'.
The source of the sounds (vocal organ) of the alphabetical letters 'b' and 'm' is one and the same: the lips. So by the passage of time 'Makkah'replaced 'Bakkah'. It can thus be appreciated that the original and ancient name of the place was 'Bakkah'. King David used this ancient name as it was in vogue during his days. It was only in the later centuries that it was replaced by Makkah.
The verse says, 'passing through the valley of Baca [they] make it a well;' Hagar passed through the valley of Baca in search of water for her son Ishma'el. Consequently she was given a well [Beersheba or Zamzam]. Those who have happened to visit this valley of Bakkah know it well that 'Ka'bah' is situated in a low lying area. Previously, when there was a heavy rain it turned into a pond. Now, a very sophisticated drainage system has been constructed there and the rain-water is quickly swept away. So every clause of the verse is perfectly pertinent to the ground realities of Makkah.
Verse 7 asserts, 'They go from strength to strength.' It depicts the zeal of the pilgrims. As they draw nearer and nearer to the sanctuary, their fervour is increased, which gives them new strength and impetus instead of fatigue.
The second clause of the verse is, 'every one of themin Zion appeareth before God' or, as NIV states, 'till each appears before God in Zion.' The word 'Zion' needs to be studied in a fair detail.
As regards its meanings, Encyclopaedia Biblica observes:
Various explanations of the name have been given. Gesenius (Thes. 1164) and Lagarde (Ubers. 84. n) derive from [a Hebrew word meaning] 'to be dry' (…) Wetzstein derives from 'to protect' so that the name would mean 'arx, citadel'; cp Zin.
Interpreter's Dic. of Bible explains:
The etymology of the name is uncertain. It may be related to the Hebrew (sayon), 'dry place' 'parched ground' (Isa. 25:5; 32:2).'
It would be appreciated that 'dry place' or 'parched ground' can be only applied to arid, barren, and sterile land of 'Makkah'. It can by no means be applied to the verdant and fertile land of 'Jerusalem'.
Like other Bible names 'Zion' may also have more than one significations. There may have been a 'Zion' of Makkah and the other of Jerusalem. But in the sense of 'dry place,'or 'parched ground'it can only be applied to 'Makkah' in the present context. It is not possible for the writer of this book to dilate upon this theme here. It may, however, be noted that the implication of the Zion of Jerusalem is to be ruled out due to the fact that there did not exist any sanctuary at Jerusalem at that time. The rest of the Psalm depicts the strong yearnings of King David to have some opportunity to visit the sanctuary of the Lord like other pilgrims.
It can thus be appreciated that as far back as the annals of history and tradition can be traced, there has been perpetually commemorated the act of Abraham's offering his genuinely 'only son', Ishma'el, for sacrifice at the mountainous area in the land of Moriah (a mountain situated in Makkah). But there is not even a single place, or a ritual, or a festivity, or a trace, or a building amongst the Jewish people or the Christians to commemorate the event of the offering of Abraham his 'only son' for sacrifice. It is now unto the reader to derive an objective conclusion.
From the perusal of the material of the chapter provided so far, it would easily be appreciated that:
i) Some 'House of the Lord of nations' already existed during the days of King David.
ii) It was a sanctuary and was abundanatly visited by pilgrims from far and near.
iii) King David had happened to stay there for a considerable period of time.
iv) It was situated in the valley of Bakkah.
v) After going back to his motherland he could not have an opportunity to visit this sanctuary due to some reasons.
vi) He expressed his earnest desire to visit this sanctuary.
vii) He envies the birds which uninterruptedly make their nests in this sanctuary and reside there.
viii) He is so fond of this 'house of the Lord' that he would prefer to be a doorkeeper there than to live in his own homeland, whom he calls the land of wickedness as compared to the sanctuary.
ix) According to him 'a day in the court of Lord' is better than a thousand (else-where).
x) The Jewish sanctuary (i.e. the Solomon's Temple) did not exist at that time. It was built by his son Solomon after his death. By that time there existed only the sanctuary of Ka'bah at Makkah, which was built by his primogenitor Abraham, and Ishma'el about ten centuries earlier and hundreds of thousands of people visited it all the year through.