Hand 1: I won many a stack by calling a button raise when I had AA and checkraising a completely dry flop. They simply assume you are restealing and move in with their KK.

Hand 2: I'm shocked you fold this to a raise pf. I don't mind folding KK37 rainbow, but with your hand you should be willing to invest a bit to play a flop, HU or not. Granted, I don't have much experience in the 400s, but if I couldn't play that hand profitably to a raise then I would rather not play at all...