Fire 3rd barrel?

[Silly String]

Villain is new to the table but loose so far. Have not seen much aggression nor any showdowns. He has played about 3 of last 6 hands.
My image is TAG, but he can't know that. We have never seen each other before.
Would you fire a 2nd barrel here and could you muster up a 3rd?
I fired 2nd barrel under the premise that he would have to raise flop or bet turn with any K. By the river, I assumed he had a weak King or 2 clubs and I gave up.

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

CO ($31.55)
Button ($24.65)
SB ($30.30)
BB ($25)
Hero ($24.75)
MP ($25.25)

Preflop: Hero is UTG with Q, A.
Hero raises to $1, 2 folds, Button calls $1, 1 fold, BB calls $0.75.

Flop: ($3.10) K, 9, 3 (3 players)
BB checks, Hero bets $2.25, Button folds, BB calls $2.25.

Turn: ($7.60) K (2 players)
BB checks, Hero bets $4.5, BB calls $4.50.

River: ($16.60) 5 (2 players)
BB checks, Hero checks.

Final Pot: $16.60

[zook]

I usually 2nd barrel here vs. a regular, maybe a little less often vs. an unknown. I never 3rd barrel.

[mixchange]

I don't like 2 barelling with 2 flush draws out as often they are calling any bet anyway.

[Da GOAT]

i try not 2nd barrel paired TPs boards

[Silly String]

i try not 2nd barrel paired TPs boards

Why not? In this situation if villain does not raise flop or bet turn, then why should I put him on a K? Unless my read is that he's that passive of a nit.

[Galapogos]

This looks like a passive villain with a FD or a K with a really crappy kicker and is afraid of a better hand, but still won't fold the river. Incidently, guys like this tilt me so much, you know what they have (or at least know how they feel about what they have), and you know they're afraid, but you know they still won't fold.