It is perfectly natural. Apart from the obvious "looks" and shallow appeal, you are well able to relate or sympathize for the character (regarding story and scripted personality). Eventually, with the sympathy and understanding of the characters personality, you can easily become attached or attracted to the fictional character. Even though the character is fictional, YOUR feelings are not.
The last time i checked, it was perfectly healthy to have feelings
The last time i checked, it was perfectly healthy to have feelings