Maybe it's just me being all dead inside, but I find it interesting when people cry to movies, probably because it hasn't happened to myself. I can get emotional and feel sadness but it doesn't express itself in that way, it's more of an inner sadness. The closest I've gotten to that level of emotion in a cinema was probably when I saw Fast & Furious 7 when they did the homage to Paul Walker at the end. Not an emotional movie by any stretch, but considering his sad fate, it was a touching homage to him and it definitely cast a big shadow over the whole movie. The movie itself was enjoyable (but not mindblowing or anything), but it became emotionally charged because of Paul Walker. I didn't cry though, but a few people did.
I think in general I get more attached to characters in episodic video-games (like Telltale or Life is Strange) or TV-shows. You get more time with the characters there, but in a 2 hour movie there's just not time for the movie to root itself so deep in my mind that I get THAT emotional about a character dying. In a TV-show however, you can have a character grow over 4-5 seasons and have a horrible fate and the impact is much bigger.