20NL: 2nd barrel on this dry board? (probably boring hand)

[Genz]

Since I vowed to pick up a more efficient session review technique, I was thinking about this spot. Is this a good spot for a 2nd barrel? The board is basically the same as on the flop and he wasn't scared of the K on the flop if he limp called with a PP and I don't know what he could be drawing at given the dryness of the flop. So give it up since he called a bet with one player yet to act on the flop or give it another shot and try using brute force?

I have only a very small sample about villain. He seems to be one of the 35/10/3 direction.

Carlos Poker 0.10/0.20, hand converted by the iPoker Converter at Talking-Poker

saw flop | <font color="#C00000">saw showdown</font>

Button Button ($23.61)
SB ($22.31)
BB <font color="#C00000">Hero ($19.90)</font>
UTG <font color="#C00000">UTG ($16.35)</font>
UTG+1 ($54.59)
CO ($19.17)

Preflop: Hero is in the BB with Q [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/spade.gif[/img]
UTG calls 0.20, 2 folds, Button calls 0.20, SB calls 0.10, Hero raises to 1.00, UTG calls 1.00, Button calls 1.00, 1 fold.

Flop (3.80) 6 [img]/images/graemlins/spade.gif[/img] 3 [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/diamond.gif[/img]
Hero bets 2.40, UTG calls 2.40, 1 fold.

Turn (8.60) 4 [img]/images/graemlins/club.gif[/img]
Hero ???