Villain 30/20/2 over small sample, that's why I called this OP PF.

Flop: I didn't think he's checking behind flop with a king after his 3-bet PF. I start thinking he may have TT, JJ, QQ, AQ, AJ. If he was bluffing PF, and wants to continue that line, he bets here. He probably has a strong hand that missed/is beaten by the king or he's given up his bluff.
Turn: Not like we have any history, but I'm usually betting half pot to start on dry boards with TP. His call tells me he probably hasn't slow played a set, but he has more than air.
River: I was contemplating making this bigger, but I don't think I bet larger on this board when I do have it. Then again, maybe I should be.

Any feedback on my analysis or play?

Full Tilt No-Limit Hold'em, $0.02 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

SB ($1.98)
BB ($2)
UTG ($0.80)
UTG+1 ($2.09)
MP1 ($2.36)
MP2 ($2.82)
MP3 ($1.21)
Hero (CO) ($2.33)
Button ($2.19)

Preflop: Hero is CO with Q, A
5 folds, Hero bets $0.08, Button raises to $0.26, 2 folds, Hero calls $0.18

Flop: ($0.55) K, 3, 9 (2 players)
Hero checks, Button checks

Turn: ($0.55) 8 (2 players)
Hero bets $0.30, Button calls $0.30

River: ($1.15) 6 (2 players)
Hero bets $0.80

Total pot: $1.15 | Rake: $0.07