AA on double paired board vs TA with strange action.

[Akimka]

Villain is TA-A (VPIP 19, PFR 8.2, postflop 3.2/1.2/3)

So his check-call => check/raise action looked very suspicious to me. If he have jack (KJ, AJ) why he didn't bet on flop HU? Why he didn't fold to my bet if he hadn't? What kind of draw he can possibly have to check-call on that board and awake when second J falls?

How would you play this hand? Differently?
And plese - provide me with hand reads - what hand do you think villain had?

Party Poker 2/4 Hold'em (9 handed) converter

Preflop: Hero is UTG+1 with A[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">6 folds</font>, BB calls.

Flop: (4.50 SB) J[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/spade.gif[/img], 5[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, BB calls.

Turn: (3.25 BB) J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">BB raises</font>, Hero calls.

River: (7.25 BB) Q[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, Hero calls.

Final Pot: 9.25 BB