$10 NLHE 6-max: AKo BvB play

In this hand I tried to play a bit tricky to keep any bluffs in. People like to think everything is a bluff in Sb vs. bb situations so I c-bet small to hopefully induce and checked on the river to let him fire any bluffs or hopefully turn KK or QQ into a bluff. When he bet so small on the turn I had to raise or the pot would be too small so I shoved. Thoughts?

BB: $15.68
UTG: $18.61
MP: $9.70
CO: $10.97
BTN: $10.00
Hero (SB): $13.25

Pre Flop: ($0.15) Hero is SB with K♥ A♠
4 folds, Hero raises to $0.30, BB raises to $0.50, Hero raises to $1.35, BB calls $0.85

Flop: ($2.70) J♥ A♣ 3♦ (2 players)
Hero bets $1.05, BB raises to $2.10, Hero calls $1.05

Turn: ($6.90) 7♠ (2 players)
Hero checks, BB bets $0.90, Hero raises to $9.80 all in, BB calls $8.90

River: ($26.50) 2♦ (2 players - 1 is all in)

no one ever turns KK or QQ into a bluff on A high boards, they just flat it down or take ridic lines but they are still playing for value

on turn you can probably make it like 4 and then just shove the rest on the river to get a crying call

4bet more. Bet flop more. Then it's an easy shove on the turn.

or this ^^

I know we dont have to balance at nl10 but I like the 4 bet size. Deff bet more OTF though. $1.50 min.

4bet size is great imo. Bet flop for around $1.40.

As played, check/shoving is pretty gross I think. The only worse he calls us with his AQ since he will 99% of the time from QQ/KK and call us with AJ/AA/JJ/AK which obv is not good

Well the small c-bet size was to try and make him think i'm bluffing. "Oh shit I have kings and an ace flopped" kinda thing. However my usual value line in this situation would be $2.11 on the flop, ~$4 on the turn and shove river, however I don't see what can continue with a line that strong hence the tricky play.