Bcb is rarely a bluff. Its usually pot control for a good but not nutted hand or someone who cbet flop, gave up on turn, and got there on the river.
almost his entire range is "something" by the river and I doubt hes turning hands like Jx, TT, and 99 into a bluff often.
yes his perceived range got stronger and that may motivate him to bluff whatever air he might have but theres just not enough air to call IMO, the reason hes motivated to bluff his air is exactly because his range got stronger, following that train of thought to a call feels like leveling ourselves to me.
I think I bet the turn but don't hate the check back, bad bad river card followed by a bet.
I think its a pretty clear fold.
and, OP, I dont think you played it poorly. I just think it went South on you, it will do that sometimes