I've found that as I age, I've become more emotional (and simultaneously better at dealing with it). I never cried in movies as a child/teenager, but nowadays I find myself choking up during particularly emotional moments in movies, shows, and life. Sometimes I just look at my son for a minute and the same thing happens. I try not to cry around people, even my family, but more because I'm conscious of the effect it has on them (upsetting or, in the case of other people, just awkward).
My theory is that, as I've developed a stronger sense of empathy and experienced more things in my life, I have a more direct emotional connection to events I witness. From what I've read based, this seems to be fairly common.