I don't see how AA, 88, or 55 could check this flop, now do I see AA not 3-betting pre. After the flop checks through, I would think he would raise the turn with KK-TT, thinking that since you checked the flop you don't have an A. I guess the other possibility is he flopped a flush, but I'm having a hard time figuring out what he could have since he can't have the Ah or Kh. I guess some suited connectors, maybe QJh?

Either way, I don't put him on a full house because the flop checked through. As for the action, I probably shove because I have pee in my pants from my post-flop excitement and I want to go change asap.