My (33F) SO (33M) tears up at so many things. It's seriously one of my favorite things about him. Hes a carpenter, and im sure his co-workers would make fun of him for it (i know he listens to podcasts at work that make him tear up in front of his co-workers). I know he doesn't like that about himself probably the same way you don't like it about yourself. But i wouldn't want him to change that. Its one of the things that makes him the most caring person, he feels things intensely.

Long story short, there are people out there that will love you for it!