Are my Kings good?

My immediate read is that the guy is just tagging along because the pot is big , and the moment you show weakness he will go all in to "big bet" you out of the pot.
A more careful second look and we see him letting you keep the lead because your bets are healthy, but on the river he's not about to let you check thus avoiding that last bet. He also has more information about your hand, your preflop raise suggesting a big pair, than you do about his.
Also that second 9 bothers me.
IMO its a fold.