Grabbed by Holdem Manager
PL Omaha $0.10(BB) Replayer
SB ($5.38)
BB ($20.92)
UTG ($7.03)
Hero ($10)
CO ($10)
BTN ($25.39)
Dealt to Hero A♦ 7♣ K♦ A♣
UTG raises to $0.30, Hero raises to $1.05, fold, fold, fold, fold, UTG calls $0.75
FLOP ($2.25) J♣ 6♥ 2♦
UTG checks, Hero bets $2.25, UTG calls $2.25
TURN ($6.75) J♣ 6♥ 2♦ 7♠
UTG checks, Hero checks
RIVER ($6.75) J♣ 6♥ 2♦ 7♠ J♠
UTG bets $3.50, Hero folds
UTG wins $6.30
UTG: 48/28, 134 hands
I'd play it the same way. UTG could have had bottom two pair on the flop, but most of the time he has a J. I like the turn check behind, as nothing that calls the flop wouldn't call the turn. On the river, I'd just fold with the overpair.
Since opponent puts us on AAxx, I expect him to fire full pot into us should he hit 2 pair on the turn since there are a few draws showing and his 2 pair is likely from a 67xx hand rather than a J6 or J7 since he raised preflop ( 67 is vulnerable to getting counterfeit on the river so can't really risk giving a free card).
I would go ahead and jam the turn, obviously as played you have to fold the river since a jack is a large part of opponents range after getting called on the flop.
That said, the line you took is fine, though it's often exploited since checking behind the turn is always weakness, smart OOP players will fire full pot into you on the river a lot of the time knowing a fold will happen a high percentage of the time. 
