Party Poker 2/4 Hold'em (9 handed)

Preflop: Hero is SB with , .
1 fold, UTG+1 calls, 2 folds, MP3 calls, CO raises, 1 fold, Hero 3-bets, 1 fold, UTG+1 calls, MP3 calls, CO calls.

Flop: (13 SB) , , (4 players)
Hero bets, UTG+1 calls, MP3 folds, CO raises, Hero 3-bets, UTG+1 calls, CO calls.

Turn: (11 BB) (3 players)
Hero bets, UTG+1 calls, CO calls.

River: (14 BB) (3 players)
Hero bets, UTG+1 folds, CO raises, Hero calls.

Final Pot: 18 BB

Results in white below:
Hero has Kd Kh (one pair, kings).
CO has Jc Js (one pair, jacks).
Outcome: Hero wins 18 BB.

I put this guy on an overpair by how he played it. Therefore, I was only losing to AA and don't think he would have played it like this. Should I have reraised on the river? I was very confident I had him but with this board. Would you often 3 bet the river in these situations? Its a minor play, but could yeild a few more big bets.