[M.B.E.]

I think there's something wrong with the arithmetic here. Your opponent started with 4260, and therefore had 4035 after posting the ante and big blind. He calls your bet of 600 on the flop, leaving him with 3435 and then the turn is checked. But you say on the river he went all in for 2000. What happened to the other 1435?

In any event, I think you should make a small bet on the river when you hit the bottom full house. Something like 800. There's a good chance you will get called if your opponent has a 7 -- he might even call that bet with king-high.

Since you did check, you do have to give serious consideration to calling your opponent's bet, since it easily could be a stone-cold bluff (busted straight draw?). He could also have the case 6 and be value-betting it.

I would certainly call the river bet if it was only 2000. If the river bet was actually 3435 I'd fold.

You can easily work it out mathematically. Let x, y, and z be the probabilities your opponent is bluffing, betting a 6, and betting an ace, respectively. Thus x+y+z=1. Let P be the pot size before his bet and let B be the size of his bet. Now your EV of calling is

P(x + y/2) + B(x - z)

so you would call if that expression is greater than zero.