I don't think you have much value in a turn raise, I probably just call.
As played, I think B/F is probably correct on the river. Hero's hand looks exactly like AT, maybe AK. Villain's line is totally consistent with KQ/KJ. It doesn't make sense for villain to C/R K9 on a river that doesn't improve his hand vs our (hero's) perceived range.
My thoughts exactly. I think the flop check / turn raise looks a lot like AT so I don't think think Villain is check-raising less than KJ here pretty much ever since he really doesn't want to get 3-bet. The other thing to consider is that he's a winning player and he cold called a raise preflop out of the SB, so presumably his range doesn't include very much (if anything) in terms of Kx that we're chopping with.
BTW OP do you play at Bay 101 pretty regularly? I play the 20/40 there occasionally although I mostly play up at AJ's.