Here's an NYT article on the function of crying. In an experiment, males who smelled female tears saw a drop in their testosterone level and in general were less sexually arousable than males who smelled a saline solution dribbled down a woman's cheek. The academics interviewed, both those who performed the study and others commenting on it, talk about the function that crying might serve -- for a girlfriend or wife to dampen a mate's sexual interest when she doesn't feel like it. One of the study's authors suggests that follow-up work could reveal a similar effect of male tears on men's aggression levels, and that crying might function to reduce aggression in other males.
It's 100% obvious that these suggestions about the function of crying are wrong, and only a moment's thought would guide you to the correct answer. But let's play naive and point to a couple problems for the theory, and then see if there's some other view of crying's function that resolves these problems.
1) The amount of time that women are not interested in sex, while their mate is pressuring them for it, is vastly greater than the amount of time that women spend crying. If crying works so well, why do they hardly ever do it?
2) As the interviewees point out, a much more effective way for a woman to say "no" is to say "no." Maybe there's some arguing back and forth, but that's more effective than crying.
To fix problem 1, is there some other group of people who spend a lot of their stubbornness time by crying? To fix problem 2, is there some other group of people who more or less lack the ability to argue back and forth, and so for whom crying would be the most effective way of communicating their displeasure?
Why, yes there is -- and they're called babies. Ever since we left a hunter-gatherer way of life some thousands of years ago, we've become more and more detached from real life, especially after the industrial revolution. One part of that is plummeting fertility rates, and the complete ignorance of human development and human nature in general that comes from not having children, and not spending time around other people's children. So it is possible for dozens of triple-digit IQ people to talk on and on about the function that tears play in an adult female dampening the sexual interest of an adult male, while never bringing up the correct answer.
Now that we've identified who the true beneficiary of crying is, why did they evolve to dampen a male's sexual interest? Parent-offspring conflict. There will be times when dad wants to make out or have sex with mom, when the baby wants that time spent on him -- feed me, protect me, and so on. The male sex drive is pretty hard to turn off once it's switched on, so the baby needs a reliably strong way to defuse dad's boner, and crying is one surefire way. Why did dad not evolve a defense against crying? Because most of the time the baby is howling for some good reason (howling is a costly and therefore honest signal of need). So if he had kept pursuing sex instead of tending to his kid's needs, the baby would have been at greater risk of dying. Such a tear-proof dad would have been genetically replaced by dads who were at least somewhat responsive to crying.
This also explains why testosterone levels fall, and why a similar study might find that male tears lowered male feelings of aggression. It would have nothing to do with what the NYT article discusses -- like an adolescent male crying to prevent others from beating him up. In fact, that works the other way -- effeminate behavior such as being a cry-baby provokes bullies into beating up on target males. Again it's babies who this is designed for, as they have no verbal way to defend themselves, and are physically outclassed by even a 10 year-old, let alone any older male. It takes someone with brain damage to beat up on a crying baby, even if he wanted to.
And it also explains why females cry more than males: in general, females are more neotenous, or resembling babies. They have more babyish faces, are more hairless, smile and laugh more, and so on. Whatever hormones or genes bring that about will also make them more prone to crying than males.
Adult males also benefit from crying in rare cases, like when they have to signal to someone who's beating them up just to teach them a lesson that they've learned their lesson and the beater should stop. A prediction from the correct view of crying's function is that adult males will be more likely to cry when they face another adult male who doesn't speak their language, and so who are back in the baby's place of being unable to argue verbally back and forth.
When lots of smart people can discuss the role of crying in helping adult females to dampen adult male sex interest, without even bringing up babies -- let alone smacking themselves on the forehead for having been so clueless before -- it makes you doubt the possibility that social science wisdom will be cumulative. Jesus, they've already forgotten the clear-as-day fact that it's babies who benefit from crying, not women.