It was only revealed in book 5 that Petunia knows about various things to do with the magical world. Dumbledore explains at the end that this is because he sent her a letter explaining about Harry etc. HOWEVER, I have a theory that she is going to play a significant part in one of the last 2 books. I also think she knows more than she is letting on.
It was mentioned quite randomly near the beginning of book 5 that her eyes are very different to Lily's eyes - perhaps just a throwaway comment, but possibly this could lead to the discovery that Petunia and Lily had different fathers or something, which is why Lily became a witch and Petunia didn't. Or perhaps Petunia received a Hogwarts letter when she was 11 too but turned it down out of fear/disgust or was expelled or similar. If they have different fathers, this could link to the long passage in book 5 where Sirius goes on about how all pure blood wizarding families are related.
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