overpair, checked turn behind, how much river value?

[daven]

Villain seems fairly tag-nittish over 100 hands at 15-10 and folding to c-bets like you get paid to do it. When he calls the flop I have trouble picking his range, mostly made up of jacks and sets I think - it''s not a very drawy board.
WA/WB situation? check turn behind?
ok, he's not gonna be checking a set two streets in a row, how much for value? I figure the jacks I'm expecting to see now are dying for the chance to pick up on my river bluff...

Full Tilt No-Limit Hold'em, $0.50 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

SB ($50.25)
BB ($117.60)
UTG ($307.45)
UTG+1 ($66)
Hero (MP1) ($50)
MP3 ($54)
CO ($150.35)
Button ($47.10)

Preflop: Hero is MP1 with K, K
2 folds, Hero raises to $1.75, 1 fold, CO calls $1.75, 2 folds, BB calls $1.25

Flop: ($5.50) 4, J, 3 (3 players)
BB checks, Hero bets $4.50, 1 fold, BB calls $4.50

Turn: ($14.50) 7 (2 players)
BB checks, Hero checks

River: ($14.50) 4 (2 players)
BB checks, ok, now what?

[Deanglow]

My god bet the turn and shove the river. As played $12

[Muzzard]

$11-12

[jimmy44]

Yup, you have to bet that turn!
Agree with Muzzard/Deanglow for the amount on river.