Not sure of this, just trying to get involved in more topics...

I guess if your three-bet range was very tight & you knew villian was aware of this you might consider 3betting to a larger amount to cut down on his implied odds.
(like its easier to call a small pp to a tight players utg raise for set value then a to a loose players button raise - so the tight player could raise to a bigger amount utg to counteract this.)

I think its a bad adjustment to make though, and a better one would be to widen your 3bet range so people cant call to outflop you & you get many other benefits as well.

At my stakes the other reasons I see people increasing there 3 bet size sometimes are...
- They have AA/KK and the original raiser was utg/utg+1 so they think
there is a good chance they will still be called/even 4bet.
- They want to fight back against a LAG who they feel is raising too often,
but they dont really want to play a pot with him, just make him fold pre- flop and make him less inclined to raise/steal in future.