capped flop made me play my AA too passively

2nd hand at table, no reads. after CO bet into me on the flop and then capped, I thought either a set or A3 (falling into the trap of thinking opponent always makes the best hand ). I think checking the turn makes sense but after villain checks thru, I think I should have value bet river but I didn't want to get raised, as I felt that any hand that was raising me would beat me. Thoughts?

Party Poker 5/10 Hold'em (8 handed) FTR converter on zerodivide.cx

Preflop: Hero is UTG with A[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/spade.gif[/img].
Hero raises, 3 folds, CO calls, [i]1 fold[/i, SB calls, 1 fold.

Flop: (7 SB) 5[img]/images/graemlins/heart.gif[/img], 2[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/heart.gif[/img] (3 players)
SB checks, Hero bets CO raises, SB calls, Hero 3-bets, CO caps, SB calls, Hero calls.

Turn: (9.50 BB) 6[img]/images/graemlins/club.gif[/img] (3 players)
SB checks, Hero checks, CO checks.

River: (9.50 BB) 5[img]/images/graemlins/spade.gif[/img] (3 players)</font>
SB checks, Hero checks, CO checks.

Final Pot: 9.50 BB