Value bet river with AA? Party 15/30

[veganmav]

MP1 is 53/8/1.1
BB is 39/12/0.8
(another great party 15/30 game [img]/images/graemlins/smile.gif[/img]
I sat one round ago.


Party Poker 15/30 Hold'em (9 handed) FTR converter on zerodivide.cx

Preflop: Hero is MP2 with A[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, <font color="#CC3333">MP1 raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#666666">3 folds</font>, SB calls, BB calls, MP1 calls.

Flop: (12 SB) Q[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, BB checks, MP1 checks, <font color="#CC3333">Hero bets</font>, SB folds, BB calls, MP1 calls.

Turn: (7.50 BB) 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, MP1 checks, <font color="#CC3333">Hero bets</font>, BB calls, MP1 calls.

River: (10.50 BB) K[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, MP1 checks, Hero..?

So everything seems standard to me until the river.
I think that BB could definately have somethting dumb like K7-KJ and be afraid of his kicker. A king seems unlikely for MP1, he probably would have played AK and KQ differently. I don't know if he's raising KJ from there preflop, and even if so, It seems like he would have showed some agression somewhere postflop.
Unlikely but still possible, there is a chance that someone either has a baby flush or is slowplaying a flush, but I'm not really worrying about it at this point.
And what are they paying off with if I am ahead?
Maybe someting like JJ or AQ but still..


So, check or bet this river? and how close do you think it is?

And if I bet, what do I do if I get check raised?