AK against tilter in BB, LP with loose preflop standards

Party Poker, 10/20

BB is on mega tilt. He's trying to play people off their hands, has showed down three or four failed bluffs in the last thirty minutes. LP has loose preflop standards, passive-weak on flops.

Hero raises from MP with A [img]/images/graemlins/diamond.gif[/img]K [img]/images/graemlins/heart.gif[/img], LP calls, BB calls

Flop: 6 [img]/images/graemlins/heart.gif[/img]A : [img]/images/graemlins/heart.gif[/img]9 [img]/images/graemlins/club.gif[/img]

BB bets, Hero calls, LP calls.

Turn: J [img]/images/graemlins/spade.gif[/img]

BB bets, Hero raises, LP calls, BB calls

River: 10 [img]/images/graemlins/diamond.gif[/img]

BB checks, action on hero? What difference would it make if BB bets?