[NL25] Folding?

Hey all, so i had two hands that i keep thinking about and where i am very uncomfortable as i dont know whats the aright play.

First hand:
PokerStars - $0.25 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 100 BB (VPIP: 46.67, PFR: 40.00, 3Bet Preflop: 0.00, Hands: 16)
SB: 38.32 BB
BB: 112.48 BB (VPIP: 50.00, PFR: 50.00, 3Bet Preflop: 50.00, Hands: 4)
UTG: 113.08 BB (VPIP: 15.38, PFR: 15.38, 3Bet Preflop: 0.00, Hands: 14)
MP: 142.64 BB (VPIP: 21.05, PFR: 21.05, 3Bet Preflop: 11.11, Hands: 19)
Hero (CO): 116.28 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has K♣ K♠

fold, fold, Hero raises to 2 BB, BTN raises to 7.52 BB, fold, fold, Hero raises to 19 BB, BTN calls 11.48 BB

Flop: (39.4 BB, 2 players) 2♦ A♣ 9♠
Hero checks, BTN bets 12.44 BB, Hero calls 12.44 BB

Turn: (64.28 BB, 2 players) 5♦
Hero checks, BTN bets 30.68 BB, fold

BTN wins 61.4 BB

Am i overfolding here? I cant get away from a feeling that he has to have and Ace or its probably possible to have set of 9.
But i may miss played my hand from the beginning here.

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Second hand:
PokerStars - $0.10 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 93 BB (VPIP: 24.49, PFR: 20.41, 3Bet Preflop: 11.76, Hands: 51)
SB: 100 BB (VPIP: 12.50, PFR: 12.50, 3Bet Preflop: 33.33, Hands: 8)
Hero (BB): 208.7 BB
UTG: 105.7 BB (VPIP: 25.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 17)
MP: 67.8 BB (VPIP: 12.50, PFR: 12.50, 3Bet Preflop: 25.00, Hands: 9)
CO: 107.7 BB (VPIP: 23.26, PFR: 19.77, 3Bet Preflop: 6.06, Hands: 87)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has A♦ A♥

fold, fold, fold, BTN raises to 2.3 BB, fold, Hero raises to 5 BB, BTN calls 2.7 BB

Flop: (10.5 BB, 2 players) 3♠ 6♦ K♦
Hero bets 5 BB, BTN calls 5 BB

Turn: (20.5 BB, 2 players) A♠
Hero bets 5.9 BB, BTN calls 5.9 BB

River: (32.3 BB, 2 players) 8♦
Hero bets 9.2 BB, BTN raises to 77.1 BB and is all-in, fold

BTN wins 48.4 BB

Here im sure that opponent could have two pairs or just A with strong kicker, but i also couldnt get away from a feeling that he had stronger hand there with shove on the river just after that flush completed.