KK set

Not sure why you call the turn against a unknown after his min 3bet on flop.
I expect he has at least 2 pair here. River is standard as played. if he had a straight it's to bad. Than you shouldn't call the turn ether if you are scared for a straight.

Cheers,
SDK1987

Preflop and flop are fine. His minbet/minraise is usually a sign he has a very strong hand, but the odds are too good to fold here and you have position on him. Turn potsized bet is him trying to get value from you. Could be he's playing a strong draw overly agressively, but that's pretty rare. At this point it seems too likely that you're beat and should consider folding. River is a nice save and easy shove. If he has a straight, so be it.

I would never call on the flop. It is always 4bet for me and try to get it in asap. I can see so many combos he can overplay BTN vs BB and lot of cards could stop action or improve his draws.

as played river is a call for me.

I overbet this flop vs fish and fold vs raise. As played click raise flop and pot turn are tells of nuts. I fold turn

Pre ok.
Flop donk is tricky, be careful l with overpairs on those boards vs BB. Probably a rec, so raise is fine. Facing a 3bet is nasty though, call and see turn however. Vs a regular, this is super super tricky flop to play.
Turn ok, but I'm really not happy, not at all. Against a very passive guy, I'm folding. KK is not the top of our range here BTN vs BB (not even close).
River ok. Blessing card, him betting 6.99 when you have 7.52 left is ridiculous, just put those 53 cents left in as you did.