i had a hand just like this recently except w/ positions reversed. opp was a reasonable player, so i checked the flop when he checked to me. he checked the turn, i bet, he folded. i like this line, b/c it keeps the pot small and it looks like AK.

out of position, against a solid player, i think i would check for the same reasons as above. against a bad player, i would make my normal continuation bet.

If I put in a good raise pf and get called with AA and the flop comes KKx, then I'm firing out half pot or so expecting him to call...and I'll do about the same on the turn: if I get raised I'm done. So many times I've seen people go way over the top with TT-QQ.