[SH] NL25 77 - set vs a nit

$0.10/$0.20 No Limit Hold'em Cash, 5 Players

MP: $32.64 (163.2 bb)
CO: $14.50 (72.5 bb)
Hero (BTN): $22.11 (110.6 bb)
SB: $20.65 (103.2 bb)
BB: $19.80 (99 bb)

Preflop: Hero is BTN with 7 7
MP raises to $0.60, CO folds, Hero calls $0.60, 2 folds

Flop: ($1.50) K 8 7 (2 players)
MP bets $0.75, Hero calls $0.75

Turn: ($3) A (2 players)
MP bets $1.50, Hero raises to $3, MP raises to $6.75, Hero raises to $20.76 and is all-in, MP calls $14.01

River: ($44.52) Q (2 players, 1 is all-in)

Results:

Villain: 16/8/2.1 within 3.4K hands
RFI EP/MP/CO/BU/SB: 6/9/16/27/7
AF F/T/R: 1.66/2.21/2.21
AFQ F/T/R: 28/32/19
CB F/T/R: 78/29(24)/25(4)
WTSD/W$SD: 25/66

Hi!
At the time of the hand I didn't realize what really tight he is and I thought it's a standard cooler... but after two days of thinking, I decided to post it here.
Can I ever fold my (bottom) set in this spot?
On the flop I didn't want to raise him.. it's a really dry flop and his cbet/fold stat is 100(3)
My turn raise was a missclick but after he 3bet me I didn't think anything else then: "YEAH GET IT IN, YOU WILL PAY ME WITH YOUR AK!!!"

Do you think he will ever have a wider range than this?

Asztal: K♠8♥7♣ A♥
       Részesedés   Nyert  Osztozás
MP2        46.59%  46.59%     0.00% { 7d7h }
MP3        53.41%  53.41%     0.00% { KK+, 88, AKs, AKo }