Learning poker again 2/3 KK out of position, double paired board

[Frogic]

MP2 in this hand is a very passive 50/0/0.19 after 30ish hands, loves to call down with any draw or piece of the board, Often folding on the turn/river after putting many bets in.

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

Preflop: Hero is SB with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="#CC3333">UTG raises</font>, <font color="#666666">2 folds</font>, MP2 calls, MP3 calls, <font color="#666666">2 folds</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#666666">1 fold</font>, UTG calls, MP2 calls, MP3 calls.

Couldn't be more standard, I'm ahead I love my equity... hoping for my none ace flop.
Flop: (13 SB) 6[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">Hero bets</font>, UTG folds, MP2 calls, MP3 calls.

Looking good so far, now anyone without a 7 or ace is practically drawing dead to me.

Turn: (8 BB) 6[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, MP2 calls, MP3 folds.

Hmm, two paired board but its the calling station so I'm betting and folding to a raise.
River: (10 BB) Q[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP2 bets</font>, Hero calls.

I really don't like my river play here, it feels like that I should have bet/folded given the opponent, since its hard to induce a bluff here and given that I checked I think arguments can be made for folding the river.
Final Pot: 12

Thoughts?