3bet pot 3way SBvsBBvsCO on broadway board

Hard spot.
I don't about many thinking players cold calling 3bet partly OOP though ^^
I think I like your turn check even though betting could still have merits. As played I think I call the river because I'm curi... hmm I mean because it's weird for him to check back better on that turn.

I think it is possible when some regs cold call pockets like 88-QQ if they dont expect the opener to make a 4bet very often, especialy when 3bet size was 8x.. I had put the opp on set, but as you said it is very unlikely he check back OTT with it...
The other scenario is to bet the turn and shove the river to bluff his sets out as I am blocking his AK straights and that probably would be a 4bet pre from him. Do you think that bluff line would work vs NL10 reg? Would he fold the set?

Indeed his range is supposed to be mainly composed of stuffs like 99-QQ and maybe strong broadways, so needless to say that he hit the board quite hard
I wonder what can he check back on the turn though. But no I wouldn't even dream of trying to make someone fold a set at NL10 lol.

I dont think he as straight, due to the check ott, maybe a set or two pairs (people like to call with connected cards like TJ).
So maybe a raise ott is in order? If he reraises we fold easily.

However, it also seems fine as played.