Against extreme LP

BB is EXTREMELY loose-passive. He'll call any raise, and play through any bets and reraises to the river. His range is huge, imo. PAHUD hasn't picked up any reads yet.

Party Poker 1/2 Hold'em (6 max, 5 handed) FTR converter on zerodivide.cx

Preflop: Hero is Button with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 fold</font>, BB calls.

Flop: (4.50 SB) J[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, BB calls.

Turn: (3.25 BB) 8[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">BB 3-bets</font>, Hero calls.
Here I am thinking he has 2 pair or 8x, given that he check/called the flop, and then 3bet the turn. I'm putting him on J8 or maybe Jx thinking the 3's will hold up for top pair/2pair.
Should I have capped given his extreme looseness, knowing we were going to go to the river?

River: (9.25 BB) J[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, Hero calls.

Final Pot: 11.25 BB
<font color="#009B00">Main Pot: 11.25 BB, between Hero and BB.</font>

Please let me know if I missed anything else or if there is any confusion.