50NL Global

HJ raises to 3x, 100bb, and is more of a recreational

Hero has AdKh on BB and raises to 11bb, HJ calls

Flop JhTh6d

Flop sizing?

My analysis here is that we want to have some checks here given IP likely has full combos of JJ/TT and probably some 66, while we have only JJ, and a small amount of TT, as some are being flatted preflop

It seems like our ranges will be quite similar, but with him maybe having a bit more offsuit combos of things like AQo.
Given all this, it seems like he will have a slight nut advantage, with our equities being similar. (first impression)

When I ran a SIM however, PIO seemed to be using a half pot sizing and betting basically range.

My action in hand was a 1/3 flop sizing, because of A) he has more absolute nuts, and equities will change alot on turn for specific parts of my range... Say overpairs on a heart, 9, T, J turn.

What am I doing wrong that my thought process is coming up with wanting to use small bets/checks when PIO is suggesting a larger bet size/and a high flop betting frequency?