KK 6max valuebet river?

Only played a few hands on this table.
How did i play this and should i valuebet the river?


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

BB ($74.23)
UTG ($42.25)
MP ($70.29)
CO ($50)
Hero ($49.95)
SB ($75.04)

Preflop: Hero is Button with Khttp://www.flopturnriver.com/phpBB2/...iles/spade.gif, Khttp://www.flopturnriver.com/phpBB2/...iles/heart.gif. SB posts a blind of $0.25.
3 folds, Hero raises to $2, 1 fold, BB calls $1.50.

Flop: ($4.25) 9http://www.flopturnriver.com/phpBB2/...iles/spade.gif, Thttp://www.flopturnriver.com/phpBB2/...es/diamond.gif, Thttp://www.flopturnriver.com/phpBB2/...iles/spade.gif (2 players)
BB bets $2, Hero raises to $6, BB raises to $10, Hero calls $4.
Turn: ($24.25) 3http://www.flopturnriver.com/phpBB2/...es/diamond.gif (2 players)
BB bets $10, Hero calls $10.

River: ($44.25) 7http://www.flopturnriver.com/phpBB2/...iles/heart.gif (2 players)
BB checks, Hero ???

Final Pot: $44.25

i cant see a lot of worse hands calling a bet here.

I check behind.

Cheque, I mean check please

Checkarooski.

I think a very small bet is ideal here, like $12-14, depending on how much you have left behind you.. anything you beat will call and anything you dont beat will most likely rr ai.