3-bet the Turn and River, or just Call?

10-Person $5/$10 Limit Hold'em on PartyPoker

Hero's UTG, Villian is UTG +1

Hero has A [img]/images/graemlins/diamond.gif[/img] A [img]/images/graemlins/heart.gif[/img]

<font color="red"> Hero raises </font>, Villian calls, 3 folds, LP calls, 2 folds, SB calls, BB calls.

Flop: Q [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/diamond.gif[/img]

SB and BB check, <font color="red"> Hero bets, Villian raises </font>, LP folds, SB calls, BB folds, <font color="red"> Hero 3-bets, Villian caps </font>, SB calls, Hero calls.

Turn: 4 [img]/images/graemlins/club.gif[/img]

SB checks, <font color="red"> Hero bets, Villian raises </font>, SB folds, Hero calls.

River: 6 [img]/images/graemlins/club.gif[/img]

<font color="red"> Hero bets, Villian raises </font>, Hero calls.

As I played the hand, I was putting Villian on either QQ, TT, or QT. If he's got QQ or TT, he probably would have 3-bet preflop, so my gut says he's got QT for 2 pair that I can beat. Should I have pushed harder on the turn and river, or did I play it correctly?