Top set oop facing river flush

Villain is solid. Plays tight aggressive ABC poker. 17/15 over 171.

I think my line is solid. His range is static after the flop. Question is about river.

Full Tilt No-Limit Hold'em, $0.10 BB (9 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

MP2 ($8.06)
MP3 ($8.25)
CO ($7.03)
Button ($5.70)
SB ($5)
BB ($24.59)
UTG ($10)
UTG+1 ($2.40)
Hero (MP1) ($10.15)

Preflop: Hero is MP1 with K, K
2 folds, Hero bets $0.40, 1 fold, MP3 calls $0.40, 1 fold, Button calls $0.40, 1 fold, BB calls $0.30

PF HJ: 22+, ATs+, KTs+, ATo+, KJo+, 98s+

Flop: ($1.65) K, 9, 3 (4 players)
BB checks, Hero bets $1.10, MP3 calls $1.10, 2 folds

Flop: AKo, AhTh+,9h8h+, 99, 33

Turn: ($3.85) A (2 players)
Hero bets $3.60, MP3 calls $3.60

River: ($11.05) 7 (2 players)
Hero?? (5.05 behind, Villain has 3.15)

My 'soul-read' is that the villains flush just got there. If he has the set or AKo i am expecting a turn shove.

c/c river, right? We are getting 4:1 if he shoves so c/f is out of the picture, no?

equity win tie pots won pots tied
Hand 0: 56.250% 56.25% 00.00% 9 0.00 { KcKd }
Hand 1: 43.750% 43.75% 00.00% 7 0.00 { 99, 33, AKs, AhQh, AhJh, AhTh, KhQh, QhJh, JhTh, Th9h, 9h8h, AKo }

Even though our psb is committing us to a river c/c, giving villain implied odds, the implied odds are still not enough to justify the turn call.