BB 3bet vs CO AKo - flop float?

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BB 3bet vs CO AKo - flop float?

Blinds: $0.08/$0.16 (6 Players) BN: $39.95
SB: $16.00
BB: $16.61 (Hero)
UTG: $10.36
MP: $16.00
CO: $22.96
Preflop ($0.24) Hero is BB with K A
2 folds, CO raises to $0.48, 2 folds, Hero raises to $1.60, CO calls $1.12
Flop ($3.28) T 4 7
Hero checks, CO bets $1.63, Hero calls $1.63
Turn ($6.54) T 4 7 2
Hero checks, CO bets $3.68, Hero calls $3.68
River ($13.90) T 4 7 2 Q
Hero checks, CO checks
Final Pot CO wins and shows a pair of Tens.
BB lost and shows high card Ace.
CO wins $13.27
Rake is $0.63

Villain: basically unknown - 50 hands, 21/19 so far - looks like normal reg

Hi, how would you play this board with AKo?

My preflop 3bet range is: TT+, ATs+, A5s-A2s, KQs, QJs, JTs, T9s, AKo

I will cbet JJ+, ATs, backdoor FD with A2-A5, suited AJ-AK with backdoors, KQs with BDFD, QJs with BDFD

Will check with any TX lower than AT, with TT because I block lot of villains continuing range + we don't need to protect our hand on this board + I will protect my checking range like this, check with A4s, and with the rest of air without backdoors - suited aces without BDFD and offsuit AX

I will X/C with TT, TX, A4s which is something like 37% of my checking range. I should therefore sometimes X/C with AKo, not everytime but like 50% of times so I wont X/F too often to bleed money.

Turn is big mistake, should be fold. I don't have to X/C hand this weak again.

But question is what strategy would you play on the flop and why ? Bet polarized range like me or cbet small with most of range?

What range would you cbet here and what sizing would you choose and why? Thanks for any ideas

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