villain is a 13/9/3 reg who i've had some battles with in the past, but nothing too crazy or recent. I think if I 3bet the flop he's only getting it in with better sets or AhKh/76hh/87hh, but i'll lose any other hands he's bluffing or value raising with.
I was thinking of check/shoving the turn but i still think he'll fold his weaker hands and draws because he isn't priced in given we're a little deep.
On the river, I'm a little worried he'll check back AK but I think checking is the only way to make more money when I'm ahead.

thoughts on all streets plz, and interpretation of his betsizing.

PokerStars No-Limit Hold'em, $1.00 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG+1 ($102.20)
MP1 ($52.50)
MP2 ($154.50)
CO ($102)
Button ($58.35)
SB ($111.45)
BB ($77.15)
Hero (UTG) ($138.50)

Preflop: Hero is UTG with 5, 5
Hero bets $3, 2 folds, MP2 calls $3, 4 folds

Flop: ($7.50) A, 9, 5 (2 players)
Hero bets $6, MP2 raises to $16, Hero calls $10

Turn: ($39.50) 2 (2 players)
Hero checks, MP2 bets $22, Hero calls $22

River: ($83.50) J (2 players)
Hero checks, MP2 bets $45, Hero calls $45

Total pot: $173.50 | Rake: $3