NL100 FR KA in SB

$0.50/$1 No Limit Holdem
8 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG ($130.55) 131bb
UTG+1 ($43.76) 44bb
MP1 ($172.30) 172bb
MP2 ($132.27) 132bb
CO ($100) 100bb
BTN ($107.89) 108bb
Hero (SB) ($358.79) 359bb
BB ($116.51) 117bb

Pre-Flop: ($1.50, 8 players) Hero is SB K♣ A♣
5 folds, BTN calls $1, Hero raises to $4, 1 fold, BTN calls $3

Flop: 10:club: K♠ 8♠ ($9, 2 players)
Hero bets $6, BTN calls $6

Turn: 3♣ ($21, 2 players)
Hero checks, BTN checks

River: 2♦ ($21, 2 players)
Hero bets $15.75, BTN raises to $68.25, Hero calls $52.50

Final Pot: $157.50

Stats in 181 hands
62/22/5.2/0/38/40
47/63/14/46/2.2

Daf*ck, I already folded a decent hand against this guy because of timeout while browsing through past hands and I regreted it because he seemed pretty agressive taking down several pots without SD and once he went to showdown with T5o, he checked on AQK, then lead pot on T in a MW and checked the river.

I just don't see what makes sense here. All draws missed and any decent hand would protect, btw I was planning to check-ship on the turn.