AKo 10/20 game. Trying to be frugal with bets?

Sorry if this is a routine hand, but I was wondering if I butchered this.

UTG, UTG+1 and a MP limper infront and I raise in LP with Ad/Kh. Folded to UTG who now raises, UTG+1 caps [img]/images/graemlins/confused.gif[/img], MP folds and I call.

Flop comes 2h/7h/10s. It's checked to me and I check behind. Good move? Bad move? I'm thinking that I'm behind to at least a pair here most of the time and don't want to get check raised here without a hand.

Turn comes Ah which I'm not sure if I'm happy to see. UTG checks, UTG+1 bets, I raise, UTG check raises, UTG+1 caps and I call thinking worst case I'm against a set of aces and a flush and I'm drawing to 6 heart outs for the nuts.

River blanks. UTG bets, UTG+1 calls, I...?

Based on the action I can't possibly see how I'm good here, but the pot is large and my hand has showdown value. Should I be finding a fold in these situations?