There's this reg at my game who opens every position with 4bb. Aside from his non-standard preflop sizing, he plays like a standard TAG on all streets.

So when this reg opens for 4bb and it's folded to me, is my calling range going to be tighter or looser than my default calling range?

Also, is my calling range going to be tighter or looser when someone limps and reg iso raise for 4bb and it's folded to me?

I'm having trouble with how I'm going to adjust when facing a larger-than-standard preflop sizing and I need help with this weakness of mine.

Can you list one reason why it should be looser in either case?

The more your opponents are risking to win the pot the more you can afford to fold. You will win more money when you wake up with a hand. Their opening range needs to be tighter to compensate. If his opening range is not tighter than normal, you only need to tighten up a little bit due to worse pot odds.

yeah, I can't think of one good reason

makes sense now, thanks

Vs larger raises, you should call less often (because you're getting a worse price on defending, so weak hands become unprofitable due to the worse pot odds), and 3-bet (slightly) more often (because there's more money in the middle).

so if my default calling range has small pp, SCs, and TPGK type hands in it and I need to tighten up my range, am I right that I should remove first the small pp and SCs because now my implied odds are not that great anymore?

should I make my 3b sizing smaller, i.e., 3x to 2.5x, vs larger open?

It's not just implied odds. You have to fold various hand types that are near the bottom of your range for calling a smaller open. e.g. a lot of Axo should also fold when facing a 4x. The smallest pairs and weakest suited connectors/gappers will also struggle vs a larger size, but deciding if K7s or KTo is more or less profitable than 22 or 75s or JTo or A8o is pretty difficult. All of those hands are close to breakeven vs a 3x, so are probably all minus EV vs a 4x.
I just press POT (to lay odds of 2:1 on a call) whatever the open-size I'm facing, but other people go larger than that when OOP. If you want to utilize fold equity, you've got to give villain bad odds on continuing. e.g. If he opens for 4x and you only make it 10x, he's not gonna fold much.

so it's more about removing the bottom of my range rather than hand type, got it

makes sense, thanks

You mean 3-bet more often relative to calling, not 3-betting a wider range, right?

If we were to plot the frequencies of the BB players response (raise (R), call (C), fold (F)), and hold the frequency of the opener players range (RFI) constant, then the frequency of R will increase as a function of increasing opening size, C will decrease, and F will increase.

This assumes some pseudo GTO. Obviously, could easily be that the opposite is true to maximize your EV vs. your opponent depending on his strategy.

I agree, however, I thought it was assumed that we were facing a rational opponent who's opening frequency would decrease as raise sizing increases.

Unless we choose to exploit based on a prior, then the GTO response will always be as stated by Arty and brokenstars, regardless of the rationality if the opponent.

Assuming that villain is opening at the same frequency for both a 3bb and 4bb open, I think we can 3-bet more often in absolute terms.

Arty and brokenstars did not say the same thing. The "GTO response" should be to 3-bet less often against a larger open, but as a larger part of our continuing strategy. Brokenstars compared a 3x vs. 4x opener with a constant opening range. If we are 3-betting more often then that is an exploit, not the GTO response.

I don't think it's as clear cut as that, and it likely depends upon positions, as well as stacksizes.
When there's more money in the pot (from a large open), so the SPR is lower and the immediate pot odds are worse, there's less of an incentive to call with weak/speculative hands, but there is more of an incentive to 3-bet to try and pick up the dead money and drive out other players. Exactly how these competing forces play out at equilibrium for every position and every stack size is impossible for me to compute.
In some positional battles it might be the case that hands that would mostly call a 3x should 3-bet vs a 4x, and in others, the opposite might be true. e.g. The SB should possibly 3-bet his entire range vs a large BTN open, but flat with some of those same hands when facing a minraise. No one has a complete GTO solution to 100bb pre-flop, so I don't think we can make blanket statements about what it looks like.

If the players at your table are playing too loose / weak, he is probably just playing correctly, and you should adjust to them, not to him. (To confirm this, check if he is winning.)

[Edit: heads up, you should adjust to him. But that's just math.]