BB is a donk and I was not worried about him. I should have said that in my original post. Also, because my check raise was so weak, I didn't give his cold call as much credit as I would have if I had raised it to $10 or more.
I was pretty sure that the villain had AA or KK. I've seen a lot of players that will min raise on the button with AA or KK if it is folded to them, for fear that the blinds will fold to a real raise.
I decided to push. BB folded. Villain thought for a while and then called. He had
and I didn't improve.
Folding on the flop seemed too weak, but I considered just calling to see if I filled up on the turn. Anyone think that's the best play?