Do I bet on the river for value?

[Reckless Rick]

Villian in the BB is a pretty passive player who plays his strong hands fast but calling down a wide range of holdings. I do not put him on a 3 or on a set that filled up on turn or river since he would bet those. Do I bet on the river? If so, which hands are calling? Does a bet turn my hand into a bluff? Is a check appropriate.

Poker Stars - No Limit Hold'em Cash Game - $0.10/$0.25 Blinds - 7 Players - (LegoPoker HH Converter)

SB: $24.75
BB: $26.25
UTG: $11.00
<font color="black">Hero (UTG+1): $50.90</font>
MP: $21.15
CO: $60.55
BTN: $25.00

<font color="black">Preflop:</font> Hero is dealt Q[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/club.gif[/img] (7 Players)
UTG checks, <font color="red">Hero raises to $1.75</font>, MP calls $1.75, 3 folds, BB calls $1.50, UTG folds

<font color="black">Flop:</font> ($5.60) T[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/spade.gif[/img] (3 Players)
<font color="red">BB bets $3.00</font>, Hero calls $3.00, MP calls $3.00

<font color="black">Turn:</font> ($14.60) T[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/diamond.gif[/img] (3 Players)
<font color="red">BB bets $4.00</font>, <font color="red">Hero raises to $10.00</font>, MP folds, BB calls $6.00

<font color="black">River:</font> ($34.60) T[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] (2 Players)
BB checks, <font color="black">Hero ???</font>