5NL FR AA UTG vs fish on double paired board

[daviddem]

MP2 is 42/0 over 13 hands, half stacked.

His range on the turn is polarized between draws and made hands that crush me. I think it's OK to bet/fold the turn? On the river there is only a half pot bet left, and his range is still super polarized between FH and missed draws (+ maybe some weird JJ or KK), so I guess I shouldn't bet here? should I ever fold if he bets?

Maybe my bet sizing was wrong on previous streets? Bet smaller on the turn?

Thoughts?

Full Tilt No-Limit Hold'em, $0.05 BB (8 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

saw flop

MP1 ($4.64)
MP2 ($2.67)
CO ($5)
Button ($6.35)
SB ($4.95)
BB ($4.26)
Hero (UTG) ($5.22)
UTG+1 ($5.33)

Preflop: Hero is UTG with A, A
Hero bets $0.20, 2 folds, MP2 calls $0.20, 4 folds

Flop: ($0.47) Q, 10, 10 (2 players)
Hero bets $0.35, MP2 calls $0.35

Turn: ($1.17) Q (2 players)
Hero bets $0.85, MP2 calls $0.85

River: ($2.87) 5 (2 players)