NL10 Value betting with AKs

Hi!

In this hand I'm not sure about whether I played the turn/river correctly.

On the flop, I think my value cbet was fine as I could probably get weaker hands like AQ-AT, A7-A2, KK-TT and maybe some 9x hands to call (while also being called by AA,99,88,98,A9,A8). Possibly also could get called by flush draws, overall though I think bet got good value.

The turn I think I should have second barrelled. The card was effectively a blank, and I think that had I barreled again I could have extracted value from a similar range as that on the flop. Would that be sound reasoning for a second barrel? What are my other options here?

With the river, I think that given I check/called on the turn, a check was reasonable. I would probably have called a bet that was half pot or less and folded to any others. Had I second barreled instead, how would you react to this completed flush? Would you triple barrell or just check/call? Or even check fold?

Thanks!!

Poker Stars $10.00 No Limit Hold'em - 6 players - View hand 1568456
DeucesCracked Poker Videos Hand History Converter

MP: $19.96
CO: $8.62
BTN: $6.83 - VPIP: 35, PFR: 15, 3B: 0, AF: 0.8, Hands: 20
SB: $10.00
BB: $22.36
Hero (UTG): $10.00

Pre Flop: ($0.15) Hero is UTG with K A
Hero raises to $0.35, MP calls $0.35, 1 fold, BTN calls $0.35, 2 folds

Flop: ($1.20) 8 A 9 (3 players)
Hero bets $1.00, MP folds, BTN calls $1

Turn: ($3.20) 4 (2 players)
Hero checks, BTN bets $2.00, Hero calls $2

River: ($7.20) 8 (2 players)
Hero checks, BTN checks