I understand the ISF theorem argument you are making here Surviva, whereby we should tend towards aggression when our range is superior to villains. Which is typically going to be the case when villain's range is capped, and ours is not. And as such, I get that overbetting turn in this hand example puts villain in a rather difficult spot whereby essentially every hand in his range is a bluffcatcher, and he's left trying to determine how frequently to bluffcatch to avoid exploitation.

The thing that has me a bit hung up is that when deciding how to size our bets, the strength of villain's range has typically always been a deciding factor (more so than the strength of my range). And I've always thought that versus a range consisting of primarily weak/marginal strength that smaller bets were typically best. Essentially, when valuebetting against a weak range, a smaller bet gives him a better price to call and means he needs to defend more frequently. And when bluffing versus a weak range, we don't typically need to bet too large.

However, at least from a GTO approach the above doesn't appear to be correct. Since, while he will need to defend less frequently to a larger bet, he's still going to be committing more money on average to do so. For instance, a 1/2 PSB means he needs to defend at least ~67% of the time, meaning he's committing 0.5 * 0.667 or 0.334 PSB on average. Versus, say a 2x PSB where he needs to defend only 33% of the time, but now must commit 2 * 0.33 or 0.668 PSB on average.