AA, opp keeps calling, value bet river? (50NL)

Opp's stats were 46/10/1.9 over 60 hands. Given that opp has $11.20 behind on the river, just put him AI or check/call? If he shoves I don't think I can fold the river.

PokerStars No-Limit Hold'em, $0.50 BB (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

CO ($48.75)
Button ($22.65)
Hero ($59.15)
BB ($10)
UTG ($64)
UTG+1 ($36.55)
MP1 ($29.20)
MP2 ($51.60)

Preflop: Hero is SB with A, A.
2 folds, MP1 raises to $1, 3 folds, Hero raises to $3, 1 fold, MP1 calls $2.

Flop: ($6.50) Q, 9, 3 (2 players)
Hero bets $5, MP1 calls $5.

Turn: ($16.50) J (2 players)
Hero bets $10, MP1 calls $10.

River: ($36.50) 4 (2 players)
Hero sees that opp has $11.20 behind and...

if you are going to call his push, you might as well push. he only bets a hand that would beat you and would likely check a hand like top pair behind you. you would lose the 11.50 if he has u beat checking/betting but he might call again with top pair so i think betting is def. the play.

I usually reraise a little more from out of position, but its no biggie. Also, raising more pre and on the flop would set up a turn push. Sometimes I just push the turn anyway even if it's an overbet since I hate these spots on the river.

As played, crying push of course.

Pot the flop, overbet push the turn. As played just push the river so you don't lose value from AQ.

Make it $4 to $4.50 preflop and get the money in on the flop and turn. The small reraise complicates things way too much.