Some people claim that Imam Zain al-Abideen has been weeping (blood from eyes) for forty years. I wanted to learn whether it is correct.
This is not a question that is directly related to religion. In any case, weeping blood is usually an expression that indicates extreme sadness and it does not mean weeping blood literally. In fact, there is no known association between being sad and weeping blood. If a person cries blood this is due to a physical illness rather than being sad.
The story of Karbala is of course a very sad and heart breaking story. It is not surprising at all to know that the son of Hussan (ra), i.e. Ali ibn al-Hussain known as Sajjad and Zayn al-Abedeen, used to cry for long time for what happened in Karbala. It seems like when people wanted to describe the extent of his sadness they would say he wept blood, and then later, gradually some people have exaggerated and taken this literally.