Counterfeited on the River?

Full Tilt No-Limit Hold’em, $20.00 BB (2 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

Hero (BB) ($5124.50)
SB ($6237.50)

Preflop: Hero is BB with 7, 6
SB bets $60, Hero calls $40

Flop: ($120) 6, 7, 10 (2 players)
Hero checks, SB bets $80, Hero raises to $299, SB calls $219

Turn: ($718) 3 (2 players)
Hero bets $555, SB calls $555

River: ($1828) 10 (2 players)
Hero checks, SB bets $950, Hero calls $950

Total pot: $3728 | Rake: $0.50

Results:
SB had 2, 8 (one pair, tens).
Hero had 7, 6 (two pair, tens and sevens).
Outcome: Hero won $3727.50

In theory, Villain should not be value betting at all thin in this spot. I am virtually always either checking to give up or checking to trap/induce with a monster. It’s virtually impossible for me to show up with a medium-strength hand here- the counterfeited two pair is really just about the only way it could happen.

The question is whether Villain realizes this, or whether he will try to value bet something like JJ (which is usually good but virtually never getting called by worse). I decided there were enough busted draws to call given the pot odds I was getting.

As an added bonus, it helped to set up this hand:

Full Tilt No-Limit Hold’em, $20.00 BB (2 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

Hero (BB) ($7989.50)
SB ($4410.50)

Preflop: Hero is BB with J, 9
SB bets $60, Hero raises to $222, SB calls $162

Flop: ($444) 5, 10, 9 (2 players)
Hero bets $287, SB calls $287

Turn: ($1018) 10 (2 players)
Hero bets $777, SB calls $777

River: ($2572) 2 (2 players)
Hero checks, SB checks

Total pot: $2572 | Rake: $0.50

Results:
SB had 6, 6 (two pair, tens and sixes).
Hero had J, 9 (two pair, tens and nines).
Outcome: Hero won $2571.50

I’m pretty comfortable check-folding the river here. I believe will Villain will often check behind his bluff catchers, as he does here- it’s an interesting question whether he ought to turn small pairs into bluffs. There really aren’t many busted draws for Villain to have, Acx isn’t impossible but I’d be surprised. If he’s calling the turn with it, it’s because he thinks it has some showdown value, so he is probably going to just check that down as well.