What a great question, and thank you for attempting to understand what to do. Without wishing to speak for all females, here is what causes me to cry.
A Heart-Wrenching Story Be it fact or fiction in a movie/book, I can get weepy over a story that touches my heart. Comfort is not needed, but some type of acknowledgement is nice that you know my emotions are in overdrive. It can be as simple as taking my hand and giving it a squeeze, or asking, “Are you okay?” Even a laugh can be acceptable if it is over something fiction-based. It helps bring me back to reality.
Physical Pain Just because you cannot see the ailment does not mean that the pain does not exist. Ask how you can help. If the response is “Nothing”, then give me time to get through it, but check in periodically. It shows that you care.
Personal Situations That Do Not Involve You These are scenarios that are so frustrating, like a work situation, that it brings on tears. Just let me talk through it. If I want advice on what to do, I will ask for it. If you have a solution that you want to offer, ask, “Would you like a suggestion?” If I say ‘no’, then let it go. I just need to vent.
Situations That Involve You If I’m a blithering mess, hopefully you realize that it needs to be addressed, but now is not the best time. Saying something to the effect of, “Let’s step away from this for a moment and come back and work through it” can work wonders.
The Death of a Loved One I really need you there to help pick up the pieces. Please be stoic, and don’t run away. Yes, we all know that each human has a shelf life with the expiration dates unknown, but it can be a very emotional time. Women just tend to let their feelings out instead of bottling them up. This isn’t necessarily a bad thing, as long as it doesn’t drag on.
Disclaimer: Again, please realize that this is coming from one female’s preferences. It does not apply to all women, nor should it be treated as a template for addressing an individual’s emotions, be the person female or male.