I suspect that there may be two classes of reason: there might be some connection to the social role of weeping, and I am fairly sure that there is a physiological role of tears in clearing both the upper respiratory tract and the eyes, of irritating or dangerous small objects, such as grit, fluff, small insects.

Tears from the eye, if they do not overflow or have time to dry out, drain down the lacrimal canals into the nasal passages. That is why your eyes water after sneezing and so on, and why you have to blow your nose after crying. You will notice that there is little tendency for the eyes to water after a smack on say, the leg.

Just don't ask me why our eyes water when we are crying; I am deeply sceptical of the aquatic ape hypothesis.