Poker Stars No-Limit Hold'em, $0.05 BB (9 handed) - Poker Stars Converter Tool from FlopTurnRiver.com

Button ($5.27)
Hero (SB) ($7.02)
BB ($11.46)
UTG ($4.75)
UTG+1 ($4.88)
MP1 ($3.24)
MP2 ($3.05)
MP3 ($5.70)
CO ($7.80)

Preflop: Hero is SB with K, A
6 folds, Button bets $0.15, Hero raises $0.43, 1 fold, Button calls $0.30

Flop: ($0.95) 8, Q, 10 (2 players)
Hero bets $0.60, Button calls $0.60

Turn: ($2.15) 3 (2 players)
Hero checks, Button checks

River: ($2.15) 5 (2 players)
Hero checks, Button checks

Total pot: $2.15

Villain is unknown, only 2 hands.

My 3-bet size pf was a mistake, I would had made it higher, maybe 55c, if I noticed that he was an unknown.
I use the 3xsize as standard, since I 3-bet "bluff" a lot vs steal-happy persons, as of who there is a lot of in zoom. My feeling is that they fold just about as much against a 3x3-bet than higher. And to keep my good hands disguised I use same 3-bet size for all. But as stated, it was a mistake here I think, since he's unknown.

anyway, as played: Do you c-bet flop here?

Why would you want to play a bigger pot OOP against an unknown?

I think you could bet turn here as well - button probably expects you to cbet here most of the time so will prob call with any piece of board, and you have 2 overs and any jack for the straight. If he calls and you miss river then I suppose try and get free showdown and take note of his opening range/call3b from button