When OOP I don't want to give the 1st caller more than 1.25:1 on his money. Too many players behind to try & "make money" on your KK.
You win less money OOP than you do IP & you lose more money OOP than you do IP. That's life at the poker table.
Since MP1's range is uncapped & you don't think he would 4! with <AA, I would raise to 2.5x the pot, which gives MP1 1.15:1 on his money. You're still going to have to call if he ships it though...unless you soul read him for AA & are certain your read is never, ever wrong....
Now when it folds to BU, if he wants to gamble it up with 63o, buy him a drink & pray he never leaves!
OTF [as played] I betting 60% - 65% pot. He's calling with a paired card & 5 outs to the Turn.
If he didn't flop 2 pair & he calls, ship it OTT no matter what the card is....unless it's an ace & you can soul read him 100% of the time for a turned 2 pair......