FR, 10 handed 100bb stacks. No reads.

I am dealt AA in EP and raise to 4bb. MP calls, Blind calls.

Flop Ac Kc 4h Pot $12

Blind checks, I bet pot, MP folds, Blind calls.

Turn Ac Kc 4h 8c Pot $36.

Blind checks, I bet $22. Is this a reasonable ammount or do people bet full pot here or push or check behind? My thinking was that he could have hit and i don't want to waste another $10-$15 and if he is calling $22 to draw to a flush he is calling $30 as well. I think it's tough for him to have an A so I discounted a hand like AxQc. I figured a flopped set would checkraise that flop, especially since I bet full pot rather than $9-$10.

What is the best way to play this turn?