Reads on villain: Notes tell me he varies his betsizes dependant on strength. So his 2x open indicates weak hand strength here, often JT, JQ type of hands. AK, AQ, AJ, 88+ would've been 3x opened.
Fold to 3-bet preflop is also 43% so way too low for his 38/23 vpip/pfr stat. Fold to Cbet is also low at 24%.

Because of those stats I already noticed one mistake in my hand, not 3-bet bigger preflop if he is going to call too often anyway. So that sizing should've been bigger.

As for the hand playing out. Preflop has been discussed, standard 3-bet, just sizing hsould've been bigger given stacksize and villain tendencies.
Flop: Anoying flop for KK but still cbetting this. Again sizing I think as I would bet my strong AX hands bigger. This villain isn't going to notice this but still good practice.
Turn: Turn card does nothing, decided to check call and get to showdown or fold. Villain bets and I decided to call given villains stats and my hand often still being good.
River: Card is another blank. Figured checking for showdown is best. Villain them overjams. Now I stopped and thought about this and wondered what Villain ever has here that makes sense. 7 is unrealistic despite his stats. His preflop 3-bet calling range is T9s+, JTo+, all pocket pairs (over a solid # of hands). So not a lot of 7's.
AK is also hard to have given there's an A on board and I hold KK. That makes another 6 combo's of AK possible. And I find this to be a very weird overbet to be making with AQ here, given that I check called turn, showing I have something, which might as well be AK for all he knows. If villain would've bet 3/4rd pot I would've believed a bit more.

So in the end, given the wide preflop range, mainly consisting of weaker hands due to the 2x raise, the low fold to cbet and the overbet on the river I decided to call.