Some of it may be physical or aesthetic attraction, but for me, it’s more personality based. Characters, or at least well written ones, are meant to emulate real people, meaning that the type of characters you feel yourself attracted to might have similar traits to real people have that you find attractive. It’s all about what kinds of personalities you like or are naturally drawn to.
Since I was a kid, I was always attracted (whether platonically or romantically) to the sarcastic, funny characters. Naturally, that same trait is one that I gravitate toward in real people to, even as an adult.