[MisterKing]

Think about this hand street by street. I think it helps you understand that you are ahead a SIGNIFICANT percentage of the time. Preflop he limps. That's not KK very often, particularly when he fails to pull the limp-reraise after you pop it. What do you see limped in EP often? Small sooted aces, sooted connectors, etc.

On the flop, your hand looks great. Of course, there are diamond flush draws out there to be aware of. The betting indicates either a slowplayed 3, medium pocket pairs (e.g. 55), a very weak king (~K6s?), AK, maaaybe KJ, even more remotely 33, or (as mentioned) flush draws. A real outlier would be AA -- but you really don't see this often. Same with KK.

On the turn, you can narrow things down a little from above. The medium pocket pairs are no longer an issue, nor are the weak kings since only a total maniac would cap those. You're now focused on (in order) sooted 3's like 53s, A3, AK, KJ, I doubt KK, and once in a blue moon 33. AA now seems like more of a possibility than on the flop, albeit still a remote one.

On the river, he's got a boat 99% of the time. The other 1% has has AA -- a small enough % to discount entirely for the purposes of our thought process. There's 1 way to make KK, 1 way to make 33, 2 ways to make KJ, 8 ways to make A3, 24 ways to make 63s-43s, and 8 ways to make AK. That's pretty much the range. You beat 32 of those combos, and lose to 12. Now, since we have no reads I guess we'd have to perhaps discount some of the 63s type hands, but still if you cut them down from 24 ways to 12 (e.g. making them 50% less likely), you still have a 20-12 advantage.

And because you have that advantage, you need to raise and reluctantly call a 3-bet. My point is, if you take the range that seems most likely pre-flop, and narrow it/refine it through each street, I think your river action becomes pretty clear.