Pocket JJ, Is A on the turn a check behind

Villain is 32/16/1.5 over 80 hands. I checked behind on the turn when the A came up, worrying that villain was playing Ax and I would get check raised. Villain then bet river and I called. Is there any benefit from betting the turn here, or is my check behind the better line?

Party Poker 5/10 Hold'em (10 handed) FTR converter on zerodivide.cx

Preflop: Hero is Button with J[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/club.gif[/img].
2 folds, UTG+2 raises, 4 folds, Hero 3-bets, 2 folds, UTG+2 calls.

Flop: (7.40 SB) 4[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/diamond.gif[/img] (2 players)
UTG+2 checks, Hero bets, UTG+2 calls.

Turn: (4.70 BB) A[img]/images/graemlins/heart.gif[/img] (2 players)
UTG+2 checks, Hero checks.

River: (4.70 BB) 6[img]/images/graemlins/heart.gif[/img] (2 players)
UTG+2 bets</font>, Hero calls.

Final Pot: 6.70 BB