Crying is partly socially controlled i.e. although a woman might be prone to tears, society will inform her as to when and where she does so. Thus, if she is having a hard day at the office, she may come home and cry to her husband, but she won't do it in front of the boss. Nevertheless, one can't get pass biology. Tears are partly controlled by the hormone prolactin, responsible for milk let down while nursing, and women have more of it than men. Emotional tears are four times as common with women as with men. To quote The Guardian:
Polling conducted by YouGov in the UK 34% of men claimed not to have cried at all in the previous year [I'm surprised it's that low], compared with only 7% of women; 18% of women said they cried at least once a week, compared with only 4% of men [I'm surprised it's that high]. Behaviour varies between cultures, but this remains a broadly global phenomenon: of 5,715 participants from 37 countries found women were more prone to crying and were more likely to have cried recently.
Human beings are the only primates that shed tears. Then again, human beings are special in that our childhood is extended and requires the care of both parents. I suppose in that case, it is important for the child to have a special method to show that it is distressed. Tears are a call for the parent to rush over and remove the distress.
As we grow up we lose the ability or, to be more precise, the threshold for emotional tears is raised. For men the threshold is very high, for a man cannot afford to be weak; the world will grind him down. But women are the weaker vessel, remember. It is quite appropriate for them to appeal for help or leniency. Think of how often a husband's anger has been turned aside by his wife's tears. Tears are the weapon mother nature has given women to protect them in their subordinate position in the home or society.
And that's the point: they're a sign of weakness, a plea for help or mercy. It is effect saying: "Don't hurt me or my feelings; I'm just a woman." A leader cannot afford to use them. A female Member of Parliament who turns on the waterworks is liable to lose respect from both women and men. They are bound to ask: just why are we electing women into this cockpit at all?