$4nl AA in the big blind

[ledfut]

I find myself getting into bad situations playing big pocket pairs on a paired board.

Pre: After calling my 3-bet, I figure his range to be AA-JJ, AK-AJ.
Flop: Standard c-bet.
Turn: Check out of fear of check-raise. Call his bet since that's about the bet size I would have made. This is the trouble spot for me. I assume the range to be about the same since I don't really have a read on him.
River: I assume I'm ahead, but bet small in case he shoves.

888 Poker - $0.04 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

MP: 74.25 BB (VPIP: 69.70, PFR: 11.11, 3Bet Preflop: 0.00, Hands: 99)
CO: 80 BB (VPIP: 24.00, PFR: 4.00, 3Bet Preflop: 0.00, Hands: 25)
BTN: 87 BB (VPIP: 44.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 25)
SB: 38.25 BB (VPIP: 40.38, PFR: 30.77, 3Bet Preflop: 11.11, Hands: 52)
Hero (BB): 122.75 BB
UTG: 108.25 BB (VPIP: 45.45, PFR: 11.36, 3Bet Preflop: 0.00, Hands: 44)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has A A

UTG raises to 3 BB, fold, fold, fold, fold, Hero raises to 9 BB, UTG calls 6 BB

Flop: (18.5 BB, 2 players) Q 6 Q
Hero bets 9.25 BB, UTG calls 9.25 BB

Turn: (37 BB, 2 players) 7
Hero checks, UTG bets 25 BB, Hero calls 25 BB

River: (87 BB, 2 players) 7
Hero bets 39.75 BB, UTG calls 39.75 BB