5NL FR flopped set vs half stack - extraction

Opp is 34 / 8 / 7AF / 50HEMAggFreq over 38 hands, and half-stacked at this point in the game.

Flop is relatively wet and hits his range, but his small cbet does not rep much strength. I think he has a lot of second pair hands here, like maybe JJ-KK or maybe some draw like QJs. I think he would cbet more if he had an A. I raise to get more money in the pot and charge draws, but I would say there is a good chance that he folds? Would just calling be OK here? Given his half stack two more streets would be enough to get the money in?

Blank turn he checks and I bet again, but maybe I should have sized it smaller, like half pot (his stack is $1.79 at this point)

Full Tilt No-Limit Hold'em, $0.05 BB (9 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

saw flop | saw showdown

UTG+1 ($2.39)
MP1 ($2.91)
MP2 ($5.79)
Hero (MP3) ($5.60)
CO ($6.68)
Button ($4.65)
SB ($5)
BB ($6.16)
UTG ($4.59)

Preflop: Hero is MP3 with 9, 9
1 fold, UTG+1 bets $0.15, 2 folds, Hero calls $0.15, 4 folds

Flop: ($0.37) 9, A, 10 (2 players)
UTG+1 bets $0.15, Hero raises to $0.45, UTG+1 calls $0.30

Turn: ($1.27) 3 (2 players)
UTG+1 checks, Hero bets $0.90