KQ on the river: value bet?

[paperboyNC]

BB is 47/7/0.66. He started the hand with only 4.5 BB and only has 1.5BB left when he checks the river. Thoughts?

Party Poker 5/10 Hold'em (9 handed) converter

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

Flop: (10.40 SB) 3[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">BB bets</font>, Hero calls, MP3 folds.

Turn: (6.20 BB) J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, Hero calls.

River: (8.20 BB) J[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, Hero ?