My son was 6 when he read the first one-the rest of them came shortly after, and then we watched the movies. He's always been pretty good with processing mature concepts like those in HP and the movies never kept him up at night or anything. (He says the only thing that scares him is jump scares :P)

We are currently on our 3rd read-through of the series, and that's just the times I've read them to him--he's read them on his own at least 3 times. I just hope he likes The Wizarding World when we go in June!