checkraised on the turn with AA

[duckhook]

I am playing 20/40 live in Brantford Ontario. UTG seems to be a solid player but I have little experience playing against him. This hand occured 2 weeks ago but for some reason I keep thinking about it.

UTG raises and I 3 bet with AA (suits irrelevent). All fold and UTG calls.

FLOP come KK2 rainbow. UTG Checks, I Bet, UTG Calls

Turn is a 6. UTG checks, I bet, UTG raises and I call.

River is a J. UTG bets and I call.

Do other people check this turn or 3 bet (fold to a 4 bet) to the check raise? I assume no one folds when check raised.

I am wondering if playing this hand differently will help me in the long run.

Thanks, duckhook