Is it strange that I sometimes cry when watching anime
What else do you do while crying?
I moan and whine for a while.
Everyone reacts differently with their emotions, and if you want to cry from anime then do so. Lots of anime stories are heartbreaking and it's great that a show influences you that much. It's great to be in touch with your emotions than be stoic and boring.
What? You don't have to make me sound like a weirdo...
I'm trying to say your normal not that you're a weirdo. A lot of people cry when watching shows. There's nothing to be ashamed of.