Trusting a Read vs. Poker Logic - 10/20 NL

[duck_butter]

Hey guys, its been awhile since I posted. I appreciate your input.

Game is 10/20 NL. My stack is 7K and Chubs to my right barely covers me. Everyone else at the table is in the 2-4K range. Chubs seems to be a pretty decent player. Hes been running really hot and caught up big time on a couple hands that he was way behind on. I get the feeling that he's tightened up a bit and doesn't want to lose the stack he's built. Bears' Fan is one of the tightest players at the table and I haven't seen him do anything crazy. I am dealt 2 2.

UTG limps, then folded to Chubs who makes it 80, I call, 2 behind me call, then Bears' Fan in the BB rr to 480. UTG calls, then chubs calls. I call with my deuces and both players behind me call as well.

Flop is K 9 2 rainbow (pot 2880)
One check to Bears' fan who pushes AI for 2900. Chubs doesn't hesitate to get his chips in the pot and starts talking while he makes the call. Based on his posture, his talk, and his mannerisms while making the call I read him for a very strong hand. He even said something about it might be time to go home, which I’ve found is very often a signal of strength.
I think for a bit and decide that I can't fold this hand, regardless of my read. So I call. Chubs and the rest of the table are surprised to see me overcall here. Usually I push here but my gut held me back.

Everyone else folds and the turn is a J (pot 11580). Chubs checks and I decide to check behind. River is a 4 (no flush) and Chubs checks again.

At this point I found myself in conflict: on the one hand my read was that Chubs was very strong. On the other hand my logic told me I must have the best hand for the following reasons:
If Chubs did flop KKK or 999, then he must know that I also flopped a very strong hand in order to overcall on the flop (and he should know I'm not a fish based on what he’s seen). I can't be calling the flop with QT or JJ. If he has 999, he should think it pretty much impossible for me to have KKK since I smooth called his pfr, then I also only called the 480 bet after Bears' Fan, another guy and Chubs all entered the pot. So my logic says that if he does have KKK or 999, then he must know that he has the best hand on the flop and subsequently the best hand on the river, but that I also have a strong hand. So how can Chubs not bet the turn and river if he has either of these two hands? He can’t be checking hoping to entice a bluff on the river because I can’t be bluffing. I can’t be bluffing because Bears’ Fan is already AI with a real hand and because there was no draw for me to call with on the flop. So because Chubs can't expect me to bet either of these streets without a strong hand, why wouldn’t he bet himself, knowing that he has a stronger hand with KKK or 999 and that he will likely get paid off because I also have a strong hand and the pot is huge?

So I couldn’t decide whether to go with my logic and value bet the river, hoping to get called by AK or K9s OR check behind based on my read that he was really strong. I also felt it was pretty weak to check behind both streets after flopping a set and this also was an itch begging me to scratch it.

So what do you guys think?