Yeah, don't lay down your KK.
I would have pushed preflop. With 4 callers of the raise there was a lot of dead money out there for you to pick up with an AI move pre-flop. Your opponent may or may not have called but you would have split.
Flop bet was fine.
Turn was suspicious. I would have bet the A like I had it to see what he does.
River I call b/c of the size of the pot.
Overall, push preflop or on flop with that hand. But overall, not a horrible play or laydown.