I'm guessing his btn stats show he likes to float? 18/11, most of the flat calling is on btn, relatively small 3bet % on btn? If so, the fact that he didn't try to steal on the turn and just called after timing a bit leads me to think he has a hand he would like to showdown on the turn (2 pair, AQ/KQ etc), likes his fd, or has a T and doesn't want to blow you off your hand. KT/KQ/KJ are the hands we're worried about (KT really shouldn't be there, but whatever), but there are a lot of other hands that play through the turn this way.
A lot of those hands aren't going to like seeing the straight complete. Depending on how much history we have w this guy and a gut feel for whether he's the type of reg who'll look for a better situation (i.e., won't want to call for a chop at best by playing the board), I like a $20ish bet on the river, fold to a raise (no way he raises without a K). If we're feeling like he can be cowed by sheer aggression into believing we were betting AsKs, $36ish might be better (bluffing that we're bluffing
, if you get my meaning). If he's a bit of a cs, I skip the bet and c/c up to 2/3psb, c/f to larger.
My image is pretty nitty at the table, the $20ish bet is enough for me to take this down unless he's holding a K or is just feeling stubborn, so this may work more often for me than for someone w more agg stats.
I'm good w betsizing on flop and turn, though curious what others think of turn betsize - I tend to bet slightly larger on the turn, $10.50 to $11.50, and I've been wondering if I shouldn't be betting smaller in that spot, $8.50 to $9.