10NL, Turned a flush but a few draws came in.

[AJGibson]

Full Tilt Poker - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 3 Players - (LegoPoker Hand History Converter)

Hero (SB): $20.35
BB: $8.00
BTN: $10.00 (VPIP around 60, 4handed for a couple of dozen hands)

BTN posts $0.10
Preflop: Hero is dealt J[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/spade.gif[/img] (3 Players)
BTN checks, <font color="red">Hero raises to $0.40</font>, BB calls $0.30, BTN calls $0.30

Flop: ($1.20) 3[img]/images/graemlins/heart.gif[/img] 9[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] (3 Players)
<font color="red">Hero bets $0.80</font>, BB folds, BTN calls $0.80

Turn: ($2.80) J[img]/images/graemlins/heart.gif[/img] (2 Players)
<font color="red">Hero bets $1.50</font>, BTN calls $1.50

River: ($5.80) K[img]/images/graemlins/club.gif[/img] (2 Players)
<font color="red">Hero bets $2.50</font>, <font color="red">BTN raises all-in to $7.30</font>, Hero calls $4.80

[Romanis]

bet more on the flop, it's drawy and you're likely ahead, make it potsize.
On the turn I also bet more, he might have a flush but a 1-card flushdraw is also possible. If you pot the flop the turn pot is 3.60, I'd push then. As played bet more, at least 3$ then you can shove the river if no heart comes and c/f if a heart comes.
As played the river doesn't matter very much because both options are bad. I'd go for a call.