He does have some AXhh in his range but I think we can bet river like half pot and expect to get called a lot by worse hands. Bet/folding obviously

You're betting large in a multiway pot and I'd give you a lot of credit for a strong hand. So much credit I over fold vs your flop and turn cbets. So my range OTR would be exceptionally strong here.

If I were in SB shoes I'd assume that the BB is probably a weaker player so I'd have every combo of QJ and many suited broadways in my range.
That said I would not call you OTR with a hand that can't even beat AK very often at all. Worst hand I would call with is probably TT. Maybe I call AhT or AhJ some times but I think that's about it.

I'm liking bet-fold line except I like a small sizing, less than 1/2 psb

If you don't think he can slowplay JQ, which I think is pretty unlikely since he should have raised turn, you should bet. The only other thing that beats you is TT which also probably would have raised turn. So I definitely think you can go for value against AJ, AT, AQ KT, A3, maybe even hands like A5-9 (if the opponent is a sticky fish).

I would go for like half pot and fold to a raise.

Smaller otf. I would x river unless vs. very big fish that I thought are calling down with AQ/AJ.