Two Plus Two Older Archives - Do I bet this river?

I have two points of concern about this hand:
1) Depending on how cagy your opponent is, by betting, you might be exposing yourself to a big risk for small gain. If he's likely to bluff, and you plan to fold to a raise, you're creating a significant chance that you lose $3k, while angling for a gain of only 500. If you're quite concerned about the possibility of a c/r, i think you should need the prospect of a bigger call to tempt you into reopening the action.

2) What was your opponent doing on the turn? I'm not really a top-level player, so i might be wrong, but it's hard to agree that he has a good read on your hand. If he does, and he has respect for your play, his $1000 would be put to better use if he changed it into $20 bills, tossed those bills into the air, and used the ensuing chaos to snag some chips out of the pot and escape. Extended imagery aside, it's hard to imagine someone calling there with "only" 99, then checking and hoping for a free showdown.

If we assume he busts you every time he hits his quads and steals the pot + a $1500 bet every time the board pairs, he only has (1/44)* $9000 + (6/44)* $3000= $615 of implied equity. This means that he has to assume that his hand is good, and will see a showdown to win, at least $485/(present pot) = 30% of the time. He would need a bigger chance of winning if he thinks you'll bluff frequently or if he plans to call a river bet.

What has changed to make him so sure of your hand by the river? I assume you would bluff at a pot of this size very frequently with this action? (maybe? don't know much about deep stack poker) If so, then he mathematically can't be *positive* that you have KK, and will probably make a crying call up to near the size of the pot.