NL25 - How to play AA on dangerous board

[Jw513]

Been at this table for a bit. Villain plays tight, 3bets pf with strong hands, and never bluffs or goes out of line.

Full Tilt No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($34.10)
Hero ($25.10)
MP ($26.05)
CO ($44.50)
Button ($15.10)
SB ($20.40)

Preflop: Hero is UTG with A, A.
Hero raises to $0.85</font>, MP raises to $2.9</font>, 4 folds</font>, Hero raises to $8.35</font>, MP calls $4.60.

Flop: ($16.20) K, 5, Q (2 players)</font>
Hero checks, MP checks.

Turn: ($16.20) T (2 players)</font>
Hero bets $7</font>, MP calls $7.

River: ($30.20) 5 (2 players)</font>
Hero checks, MP checks.

Final Pot: $30.20

At preflop, villain insta-3bets, but he took like 15 sec to call my 4bet. I didn't like this flop, because I lose to QQ/KK, which he can easily have. He checks behind on the flop so I'm thinking he doesn't have KK/QQ. At the turn, I decided to make a small bet to see where he's at. He calls. I put him on AK/JJ now. I think if he had a set he would have raised by now. River goes check check. I had $10 left and was going to call any bet, based on my reads, and pot odds were good. Did I play this well? Anyone prefer a check on the turn?