[Rush17]

I would check/call on 4th. By betting, you're telling him that you have AA (or any high hand), and that will make it easier for him to outplay you and/or to make less mistakes. Let him think you bricked on 4th(it's not as if you're going to miss out on a bet because most players will bet their boards in that spot)and take it from there.

If you check/call on 4th and he catches good again on 5th, I'd seriously consider letting it go although calling to see one more card drop *on his board* (YOUR board is not relevant) would probably be Ok, too. But, I don't like that you bet into him on 5th because now he knows that you have a high hand, and, you stand a great chance to get raised. Question, would you have dropped your hand had he raised you on 5th? If you would have, then I don't see the justification to the call on 6th. It's time to say goodbye and save 2 big bets, I think.