How do you play this spot when you have AK/AQs? If you go for a x/c or x/r then x/f here could be good.
You need to be quite sure he'll fold JJ/TT to a 4bet tho. Consider you are blocking 8 of his AK combos.

I think I'll prefer a small blocking bet, about 1/3 of the pot.

i would play it like u did and x/f flop . if OP had some more $ behind i prob would go for a 1/3 bet.

It's possible for him to call a 4bet much wider than just QQ+ and AK as he will have position on us. When you check an ace high board here, villain could certainly stab with his QQ-99 hands, so i wouldn't immediately give up on the flop. Furthermore, with two kings in our hand, the probability of villain holding exactly AK goes down significantly.

Let's construct a range for ourselves here. What hands are in our 4betting range? Let's for arguments sake say its JJ+ and AK. What hands are we c-betting and what are we checking? We probably only want to be betting with AK for value, and checking the pairs. AA blocks alot of the hands we want to get called by, and the others just want to get to showdown. So when we check the flop, villain can often assume that we don't hold an ace.

I would call flop. We will have AA in our range here, making it tough for villain to fire twice with a hand like JJ or TT. Against continued aggression i will be folding.

In hindsight would probably go 1.10 pre and make it 1/3 on the flop. Depending on how you construct your 4betting range in this position, I'd imagine you are quite low down in your range on this flop. If you call, there's about 2$ left into a pot of around $6.40. I also don't think population bluffs this spot enough so would make a nitty x/f

4bet is way too big. You need to give your opponent a chance to call with hands weaker than QQ. I'd usually make it something like 1,25. Just calling preflop is also a fine option since there's not really all that much value in 4betting againts a tight 3betting range from these positions.

Flop is well done.

Even with an A we don't like on the flop, I still like to bet 1/3 to avoid c/f and still getting value from some low PPs that still can get a call with an A on the flop.

If vilain calls we simply check down and hope he doesn't bet later.