10/20 - KK - tough board; overcall river?

[Hoi Polloi]

HJ is 35/25/1.1 over 125 hands. Cautious post-flop.
BTN is 42/15/1.4 over 500+. A loser in the game and can bluff wildly or be a calling station as his mood (I suppose) dictates.

I'm in the SB with K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/club.gif[/img].

10/20 LHE 6-max, 6 players

Pre-flop: 1 folds, HJ opens, 1 fold, BTN calls, Hero 3-bets, 1 fold, 2 calls.

Flop (7SB, 3 players): A[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/club.gif[/img]
Hero bets, 2 calls.

Turn (5BB, 3 players): T[img]/images/graemlins/spade.gif[/img]
Hero bets, 2 calls.

River (8BB, 3 players): 4[img]/images/graemlins/diamond.gif[/img]
Hero checks, HJ bets, BTN calls, Hero?

Do you make this overcall?