Of course, crying being a signaling mechanism is another explanation. Maybe a better one.
The only other connection I can make is that migraines are closely correlated with dry eyes (and emotion can trigger migraines.) So people with migraines are sometimes advised to use eyedrops to reduce migraine incidence these days. Lacrimation is also a migraine symptom. If your brain is very active due to emotion, maybe tears help to reduce the chances that migraines result? (Or returning to the first hypothesis, maybe CSF pressure is elevated during migraines.)
Not a disproof, but chimps are more socially sacrificing than this article indicates, they will find crippled chimps for long periods, as a group; IIRC not just relatives.
The only things I could find about migraines and dry eyes were positively correlated, but not strong, and not enough to be causative. Can you share more sources? Also, most source indicates IIH can be comorbid with migraines, but is unrelated, curious if you have sources to share on that, too.
The I believe very recent study I saw found a high correlation. I've heard anecdotal reports of eyedrops helping; it's too soon to find studies of (neutral) eyedrops helping, but you can find preliminary studies of migraine treatment beta blocker eyedrops at pubmed dot com.
No tail wagging dog - it's common for studies about one thing to discover something interesting that's consistent with quite another hypothesis (which is the most evidence can be, qua Popper.) That's all I've claimed in this case. There was no such correlation with saliva, so it's clear that disproof was risked - the Popperian litmus test for actual evidence.