I think betting the flop is fine. I usually go smaller here, something like 6$. Paired boards can be confusing because people at those stakes usually have very unbalanced strategies on them, either folding too much or being too sticky/bluffy.

A small bet allows us some protection and immediate fold equity against the part of his range that he's folding. A lot of hands in villain's range will have very low equity and will not be priced in to call.

You will have enough fold equity to make it profitable, and we have equity when called. Then if the turn bricks I think we should check. Villain's range on the turn is such that betting with AA doesn't make much sense anymore. He's not gonna call down with worse and we have very bad equity against the top of his range.

On this particular turn I feel comfortable check/folding when readless. We have a good amount of KK in our range and I will check all of them on the turn to allow his floats to bet. I know that this is exploitable but I call it exploitable with a safety net. Why?

When I fold I take a note that he called me on a paired board and bet the turn when checked to. Next time a similar spot comes up I am going to keep him honest and call down. This is my safety net. If he had trips both times, he's due to get paid once. But what's more likely happening is that at least one of those was a float, meaning he's not playing a completely straightforward strategy, thus calling down has merit.

This is my personal approach to those spots when readless.

Love the note takin spot, just wish my notes werent already 3 pages long for most regs.