I'd probably put him on something that is not folding the river.  And I wouldn't be too sure about him leading with boats or not.  Players kinda seem to like to do that differently.  A _LOT_ of players seem c/c or c/r happy more than their fair share.  But whichever line they prefer with their boats, they tend to be extreme towards one play or another.  So player notes are useful.

What he probably doesn't have on the turn though is a straight.  That leaves hands that made boats on the river, and missed flush draws.  The boats won't fold, and some of the missed draws you beat, so I think checking back here and giving up is the best play.

I don't think that your line reps value particularly credibly on this river. While we could possibly have raised sets (maybe some 2 pair??) for value on the turn given what we perceived as weakness, we almost certainly wouldn't have checked back flop with them on this board. Would betting ~80% pot be your standard with AJ here? It would seem pretty optimistic to me.

Also I think that we have enough showdown value with JJ here that we occasionally win vs some kind of flush draw. There are probably some other bluffs you get to the river with that would be better using when you do decide to follow through.

Although I haven't worked on these kinds of things like others in this forum have I would guess that the river is better for villain's range than ours (especially as we have no read on what he does with boats) and that should probably make us less inclined to be betting it in general.

I'd just say that he has way less straights that boats.

I'm not betting vs reg here. mb vs some losse-passive player who get there with 2many weak combos K8, KT, J9, some pair +gutters.