You guys all seem sure it is a vb but imo it is really close...

I think I would bet really small. Something between 150 and 250 on the river. On the river his range is imo Jx, 7x(A7, K7, maybe Q7), 6x (A6, K6), Adx, Kdx. There is not much in his range that calls a river bet and loses to our J6 here : Jx prob call, K7, Q7 and K6 prob folds. All the rest is either a fold or a call (then we are beat)
That's why I think it is either a small vb (to keep 3rd or 4th pair in his calling range) or a check back.