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On parting ways with her nephew Harry, probably for good, Petunia continues to be her same old self; she fusses over and adores Dudley, while being cold and disinterested in Harry. But then, at the last possible moment, we see (maybe) a glimmer of a heart in the woman:
She stopped and looked back. For a moment Harry had the strangest feeling that she wanted to say something to him: She gave him an odd, tremulous look and seemed to teeter on the edge of speech, but then, with a little jerk of her head, she bustled out of the room after her husband and son. (3.121)
What was she going to say?! Well, we never learn in the book, but after publishing Deathly Hallows, Rowling revealed what Petunia was thinking:
[…] [Petunia] almost wished Harry luck when she said goodbye to him in this book, she just teetered on the verge of saying, I do know what you're up against and I hope it's OK. But she couldn't bring herself to say it. Years of pretending she doesn't care have hardened her. (source)
Though we don't see any more of grown-up Petunia Dursley in Deathly Hallows, we do meet her as a girl, Petunia Evans, through Snape's memories. We see Petunia and Lily as Lily learns she's a witch. From these memories, it seems that Petunia is terribly jealous that her sister is a witch, while she has no magical powers at all. Really, Petunia just wanted to go to Hogwarts too, but got left behind. If she hadn't married the awful, mega-Muggle Vernon Dursley, maybe she wouldn't have been quite so bad?