I have recently dedicated some more study time into overbetting the turn. There are several sources here on RIO that cover this topic (e.g. Peter Clarke's FTGU course and two Essential videos by Steve Paul) and they agree that overbets as the PFR IP happen in the following situation:

1. We have c-bet the flop as PFR IP
2. the OOP player was incentivized to develop a XR range OTF but did just call
3. the turn is a blank/does not re-distribute nut advantage

I am experimenting including overbets in my game currently and I like them quite a lot. What I am still wondering is how we behave if the turn pairs one the flop cards? I'm unsure whether these are overbet spots or not.

When the top card pairs (e.g. BU vs. BB on J82ss Jx)
This should be in favor of the PFR's range, right? Quite some Jx combos of the PFC now moved ahead of our overpairs, however we have many more Jx as the PFR. We have more AJ-KJ and JJ (since parts of these holdings would have 3-bet pre), and J8 since the PFC might have XR these OTF. So is it a favorable overbet spot in general when the top card pairs?

When the middle card pairs (e.g. BU vs. BB on J82ss 8x)
Here I would say that this should favor the PFC's range. Sure, the BB might have 3-bet 88 pre so quads are discounted from the PFC's range but this is only one combo. In general, the PFR is inclined to check back middle pairs on such a flop. The PFC will c/c a lot of them vs. a polarized c-bet range as employed on this board and hence has the 8x advantage here. So it is not a favorable overbet spot when the middle card pairs?

When the bottom card pairs (e.g. BU vs. BB on J82ss 2x)
Here I'm actually very unsure how this changes equities. In general, I would also say that this turn favors the BB's range as the BB is going to have way more 2x than the BU (BB defends K2s, Q2s and maybe even J2s) while the BU not necessarily opens all of these. However, I'm unsure whether many 2x are actually in the BB's c/c range to a c-bet. Do we employ overbets when the bottom card pairs?

Any thoughts appreciated...