To be honest, I'm taking a different approach here. Instead of the math or equity which sometimes we get obsessed with, I just want to look at the streets and hands he can have.
Pre flop hes calling a 3x from the BTN against you UTG. Yes hes looser here, but not crazy loose. I do not believe all of the offsuit K10 combos are here but all of suited ones are. QQ and AA aren't here, both of those hands are 3-betting almost always since the image of the BTN is to raising a little lighter. Does your opponent really have 109 off here (later streets will explain why)? Thats way too loose in my opinion to be calling and the only combos are 109 suited if that. AJ for sure and AK is also viable, but I think AK raises from the BTN (but some will flat, so lets leave it). QJ for sure, and I think 22-JJ is all possible here as well, along with some combos of KX suited,AX suited, JX, diamonds and a few others of course.
On the flop, two diamonds, very connected clearly. UTG bets 2/3 and the BTN flats. This discounts all the pairs he could have except JJ and MAYBE TT, except given his stats I doubt TT with the T of diamonds is calling here. K10 is still here, as well as 109 combos and all the diamond combos and hands like Q10 and MAYBE J10 runs one off but given stats im not sure.
Now the turn is an 8 of clubs which rarely improves the villian. We again bet almost 2/3 pot. Does K10 flat again? Or 109 flat when it hits? Why would you want to let two pair run another card for free or AK (if you have 109) to get a chance to counterfeit you for cheap?I do think K10 sometimes flats for value and you have blockers to block a split, but why do it for a cheaper price? That story doesnt make much sense as if we did have a massive hand like KQ of diamonds, we cant draw for cheap ever and the BTN has to know that. You are showing WAY too much strength to let your hands potentially catch up. Even if he had JJ, it makes even less sense for a set to not raise here as JJ is so vulnerable to hands that even you can have like K10 suited or two pairs that look to improve him on the river (like if another Q or A ran off on the river) but it actually kills him. I just don't see the view in flatting a ton of his range here, and he cant have KQ of diamonds (you block that) and he cant have anything that really is a monstrous draw since those hands are all basically blocked EXCEPT K10 of diamonds, thats it.
River is a 7, which is a blank to you. You again bet big, and he jams the river. What about this story makes sense? How does he jam JJ if he did have it when he can be dead? AJ, QJ, AK most likely just call, and so many missed hands fold. But his bluffs (diamonds) may feel the only way he wins the pot is if he jams it in, but so much of this range is gone on other streets. He doesnt have A hand like A10 of diamonds since its blocked, QX diamonds into a bluff is blocked, same as JX. So this limits his range to what? K10 combo or more specifically of diamonds, or an overplay which is actually a bluff of AJ or AK maybe even A8 of clubs or something like that. You just show so much strength that the range on the river is so thin that, in my opinion, he had you dead from jump street or you have him beat and he feels there is too much money to give up in the middle. I would have called I think for sure, just because I do not believe this story at all given the texture of the board and given how many hands he cant have going into the river. You also have particularly good pot odds
to call, which may be more enticing to run it off as well.
Just my take on the hand, good luck!