The river play is missing from the hand.

How do you know he's got that jack? From his flop raise/call and his loose PFR/AF stats, he could have played that way with 99-QQ, or AJ-A9. Maybe QJs. (A real, non-stat read would tell you if he's capable of a bluff/semi-bluff to put you off overcards, which would open up his range even more.) With his aggression over a large number of hands, I'd see him capping the flop with 99, JJ or AJ, especially JJ since BB is obviously coming along for the ride.

After the turn I toss 99 and JJ (unless he's a devious fella) and have him calling down with everything else in his range. The A adds back in A9 as something to worry about, but I still think you beat most of his range here. BB is more worrisome, but as you say, he could have anything, so I'm not going to fear the flush monster.

I'm making the value bet.