i think that petunia likes and cares for harry as a person , but the dislike and hate which he recieves from her is because of what he is and what he stands for..i think petunia was very jealous of her sisters gift and that she developed hatred for her sister because of her magic ...
i think dumbledore told petunia what magic was in place in her blood and she agreed to keep him as she likes him as a person but not for what he is or what he stands for ( a wizard)