Preflop
You are 60BB deep, and for that reason I prefer to go bigger than just a min-raise. Facing the 3-bet you cant fold, but it is at least a consideration to 4-bet jam to try and get it heads-up with BB and go for his bounty. I would be more inclined to do so however if it was a SB 3-bet, and/or stacks were a bit more shallow. So I guess, its fine to just call and see a flop, even though you invite BTN to dubble flat and take position on you.
Flop
When BB - the preflop 3-bettor - check this flop, you are good against him the vast majority of the time, and the stack to pot ratio against him is only a little more than one. Also other than flopping a set this is pretty much the best flop, you can hope for, and at lot of the time BTN would have 3-bet TT+ instead of just flatting. So while you might be behind to him, its also kind of unlikely. At the same time you hand needs a lot of protection, since two opponents can have as many as 12 outs combined to hit a higher pair. So for me this is a mandatory bet when checked to, and if either player raise, then just get it in and hope to run good.
Turn
Now the hand gets extremely silly, since BB bet 7% of the pot, and BTN raise to 20% of the pot. You cant really take aggressive action now with the K on the board, so as (mis)played on the flop its a sigh-call and hope, they check the river or make another silly small bet, so you can get to showdown.
River
As played you cant call an overbet now. Even though he showed you a bluff, its still a good and solid fold. The mistake was not betting the flop for value and protection, which would likely have caused him to fold, and in that way you also protect yourself from getting bluffed on later streets. Or being a little results oriented after seeing BTNs hand go for the hell-Mary 4-bet jam preflop and force him to either fold or play a "flip" for all your chips. He is a loose player according to the build-in HUD, and in a PKO this kind of player might even call with hands, that 99 dominate.
