Hand History driven straight to this forum by DriveHUD - http://drivehud.com

NL Holdem $0.10(BB)
BTN ($7.64)
SB ($9.9)
BB ($10.15)
HERO ($12.06)
HJ ($10.77)
CO ($9.95)

Dealt to Hero Ad Js

HERO Raises To $0.34 (Rem. Stack: 11.72), HJ Folds, CO Folds, BTN Calls $0.34 (Rem. Stack: 7.30), SB Folds, BB Folds

Flop ($0.83) 9h Jc 4d
HERO Bets $0.41 (Rem. Stack: 11.31), BTN Calls $0.41 (Rem. Stack: 6.89)

Turn ($1.65) 9h Jc 4d 5h
HERO Bets $1.22 (Rem. Stack: 10.09), BTN Calls $1.22 (Rem. Stack: 5.67)

River ($4.09) 9h Jc 4d 5h Kd
HERO Checks, BTN Bets $2 (Rem. Stack: 3.67), HERO ???

I don't like how I played this hand up to this point. Checking the river seems bad because it gives him a chance to bluff/value nicely balanced and deceptively as he did here. Still, now that we're here, do you put enough Kx and sets in his range given river card that I can make an exploitative fold here or is this a clear call?

As always, input and advice is greatly appreciated.