Hmmm good question. It's difficult to pin-point who does it the most, although it's probably more from males. The time in my life where it was most prominant was in highschool/college by primarily other males, however it hasn't died out much as people get older.
I generally get the impression that more aggressive males tend to try to influence other males to suppress the emotions outside of aggression. I am curious what the experience is from other men and boys, since I'm coming from a completely different perspective.
Very rarely have I seen a woman/girl be ridiculed for crying, in the sense that it's not something their sex is supposed to be doing.
I know this is only anecdotal, but to me it seems to be that if a Woman cries it generates sympathy, if a Man cries it generates ridicule.
On certain occasions, yes. Crying in either gender is generally seen as weakness. What I've come across is that though in some situations if a woman cries it generates sympathy, unless she is in an active caregiver mode. I've heard women chide other women if they cry or "show weakness" when they are caring for a sick or injured child, or an aging parent who might be terminal. In those situations, I've generally seen it to be forgiving for men to cry, which I have seen generates sympathy from others, but it seems expected for women to remain strong and to be there for those who are hurt, ill, or dying.