I think this is a somewhat interesting question which I've heard a couple competing perspectives on. 

From a GTO standpoint, in which case does the BB have a higher 3-bet frequency (assume the SB folds), when the Button opens to 2bb or Button opens to 3bb. Assume the Button is opening a GTO range in both cases. Assume that we 3-bet to the same % relative to the open (ie we pot our 3-bet in both cases) And why?

I've heard lots of strong theoretical posters say that they're 3-bet frequency is higher when the Button opens to 3bb because there's more incentive to 3-bet because they win more when the Villain folds. And that it's easier to call with hands when the Button opens to 2bb because we're getting better odds to call. 

I think that our 3-bet frequency would be higher when the Button opens to 2bb because the Buttons opening range should be wider because since he's risking less, he can open wider. When he opens wider, we can 3-bet for "value" thinner which means that we can include more bluffs as well. And thus our overall 3-bet range will be wider. 

Haven't really thought much about it, and since I've heard lots of strong players suggest otherwise, I thought it would open an interesting discussion.