I think big flop beats aren't that good on this board. By betting big you cutting his range to Kx,PP and FDs which only make sense with probably exact hand you holding for value.
You can say why Jeff_ not put a lot of money and win a lot whenever he has K, it is not black in white. EV of betting small is high as well(can be higher/lower) since you get action/value from weaker hands and still can put big river bet on some runouts.

Would call river, Kh is pretty powerful since we block Kh5h Kh4h and his value range something like 44/55 (6) K5-K4(1+6)+KQ(3) and I'm not even sure that 44/55 willdonk jam river so his range is faily narrow.

Any info into what kind of player this is?

I don’t think he has many missed FD here after calling two large bets oop on a paired board. He is donking 2x pot into a very strong looking range. If he has 11 value combos, he needs 7.5 worst “value hands”/bluffs to breakeven call. It’s possible K5o exists if he’s on the looser side. Even if he did this with all KJ, that’s still only 4 combos. I don’t think folding is that bad here unless he is capable of bluffing/spazzing