Fold the 2nd nuts?

Villain was 9/7 - I repeat, nine-fucking-seven.

Outrageous tightness was the reason for the preflop flat-call, I don't think he can call a 3bet with much worse and of course in this spot I only have the BB behind me to worry about it going multiway so I'm not so worried about that. Maybe everyone hates the flat? It seems kind of odd on review, but I felt like there was a valid reason to do it here.

I decide to check the turn and take a free one off if I can, as I think Qh strongly improves his range here and when he barrels I'm probably folding the river unimproved.

But we bink the 2nd nuts - given that villain is so tight, can any of you fold the river here?

Poker Stars, $0.10/$0.25 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

BTN: $25.47 (101.9 bb)
Hero (SB): $63.77 (255.1 bb)
BB: $19.64 (78.6 bb)
UTG: $58.84 (235.4 bb)
MP: $26.98 (107.9 bb)
CO: $9.84 (39.4 bb)

Preflop: Hero is SB with K K
3 folds, BTN raises to $0.80, Hero calls $0.70, BB folds

Flop: ($1.85) J 2 8 (2 players)
Hero checks, BTN bets $1.20, Hero calls $1.20

Turn: ($4.25) Q (2 players)
Hero checks, BTN bets $2.90, Hero calls $2.90

River: ($10.05) 7 (2 players)
Hero checks, BTN bets $7

Hero?