Our villain is betting more than he should, but instead of maniacally overbluffing, he's actually adding thinner value bets everywhere so he always ends up with the optimal value to bluff ratio. How do we counter this guy?

Trap into them more and raise at a higher frequency.

When they check bluff more because their check range has a higher frequency of trash

Yeah it sounds like he’s gutting his checking range so when it goes check check you can probably bluff him more

Bluffing more works well in practice, but in theory villain could just start overcalling to exploit your overbluff. Yes his range is capped, but he can still compensate for that by calling down all his weaker bluffcatchers.

A better way of attacking his checking range is to size up with the appropriate value hands. This naturally has the effect of allowing you to bluff more, although the actual ev increase will come from your made hands, since they are getting more value.

I assume we would also have to size up some of our bluffing hands.

Yes of course

Check raising more is also effective. You can expand the value portion of your check raise range and add corresponding bluffs.

In practice those thin value bets are difficult to defend against aggressive check raising followed up by additional barrels when appropriate.

I agree with this:

They need to weaken their checking range to bet more often than GTO while retaining balance, so they attack their checks more aggressively.

They'd also need to be putting in more money overall compared to GTO (assuming their sizing remains the same). That means you have more incentive to trap with your nutted hands. So slow play more often.

This is not opponent who you can exploit by much.
But as already said, you can raise thinner for value, bet bigger and thinner for value when he checks. If he over folds you bluff a ton, but this is not guaranteed by his wide betting range.

It can be exploited a lot. They are spreading out too thin and somethings gotta break.

I would structure my thought process in a series of hypothesis like this:

1. First exploit is to start inducing with STRONG hands that beat a lot of his thin value. Inducing with bluff catchers does nothing whatsoever.

2a. His passive lines are unprotected -> Overbluff after he checks
This point could be proved wrong by him showing a low fold after checking

2b. His passive lines are unprotected, but he stations anyway so he doesn't overfold -> Bet ridiculously thin against his passive lines
This could be shown by him making pretty light calls after checking

2c. His passive lines are actually protected enough by strong hands, but seemingly still bets way too thin and bluffs a ton himself -> Become very aggressive against his bets
This could be shown by him having a low fold and not seemingly making ridiculous calls after checking

Versus 2b and 2c -> Play tighter preflop.

If you correctly asses what his range construction problem is and address it properly, you will crush a player like this unless he is good at re-adjusting and switching gears

villain can always adjust to your adjustments lol that's not the question