$10 NLHE 6-max: AA V fish, semi-draw heavy board

I'm pretty sure that getting it in here is never a major mistake however I'd like some opinions.

Notes: Villain has called down big bets by HERO on the flop and turn OOP with 22 on 4,5,5,9,6 TTTT board after limping in the pot and getting raised by HERO.

Hand sample: 64 Villain Stats: 43,13,1.3 Raise c-bet - IP: 0 (2) OOP: 50 (4)
Villain holding a straight draw played aggressively (0/1)

poker stars $0.05/$0.10 No Limit Hold'em - 6 players - View hand 2186499
DeucesCracked Poker Videos Hand History Converter

SB: $13.00
Hero (BB): $10.52
UTG: $20.27
MP: $10.00
CO: $10.00
BTN: $22.60

Pre Flop: ($0.15) Hero is BB with A :club: A :spade:
3 folds, BTN raises to $0.25, 1 fold, Hero raises to $0.85, BTN calls $0.60

Flop: ($1.75) Q :diamond: 6 :club: 7 :club: (2 players)
Hero bets $1.25, BTN raises to $2.50, Hero raises to $9.67 all in, BTN calls $7.17

Turn: ($21.09) Q :spade: (2 players - 1 is all in)

River: ($21.09) 6 :spade: (2 players - 1 is all in)

If he doesn't raise draws then I would suspect a set. Still, can't fold the Aces against a fish unless you are pretty damn sure.