Well, I think it's obvious that she's jealous of her sister.

I think that she's jealous because Lily's a witch and she's not--well, not because Lily's a witch, but because of all the attention she received for it.

Think about it: You're a child with a sibling. Suddenly, your sibling gets accepted to a wizarding school, and your parents are overjoyed! I'm sure anyone with a sibling can at least sympathize a little with Petunia's feelings, though she takes them a bit far, I think.

I think Petunia's current hate of everything magical stems from her being overshadowed by Lily's accomplishments.

It's also why she treats Harry so poorly. He's a constant reminder of everything her sister has accomplished...and everything she hasn't.