That’s an excellent question.
About an overweight player, well it’s her problem, but I have to say I find it unprofessional and disgraceful for her sport. A professional athlete, man or woman, should be fit (well, maybe not a sumo wrestler
Regarding her personality, honesty and integrity are extremely important to me. I could never stand for a blatant cheater, let alone a murderer. In my opinion, an athlete cannot be dissociated from her personality. If I can’t respect her as a person, I can’t root for her on court.
I don’t really care if a player is lying to herself about her fitness or skills. Or about where she should stand in the ranking. And its fine is she’s lying to some fans or Medias in order to protect her private life.
But I expect her to be respectful towards her fans, the crowd and her opponents. I don’t care is she breaks her rackets, kick a wall or talk to herself aloud, but I do care if she’s rude with the ballboys or threaten her opponent.
Fist clenching close to the body doesn’t bother me, because it’s a personal celebration. Showing your fist to your opponent’s face does bother me, since I find it disrespectful. I must admit that I analyze these behaviors in regards to the player general attitude. I forgive a lot of things to a player if I think that she is a genuinely nice person (Ana Ivanovic, for example, whose antics doesn’t bother me).
All in all, yes I can become a fan of a player if I appreciate her personality, as well as I can stop rooting for another player if I find her unpleasant.