Honestly, both sides have a stake for and against it.  On the liberal side, you have your typical fat SJWs/fedora tippers/lesians/feminists.  On the other hand, you also have the more health conscious types.  Meanwhile on the conservative side you have the typical fat religious evangelical types, but you also have the "take some personal responsibility for your own goddamn actions" types.  I'd be hard pressed to say which side is more highly invested in fatties.