This is an example of a typical situation where I tend to struggle often between my options and the way to compose my ranges.
Roughly speaking, I'm reasonably far ahead of the 3bet-range, yet far enough behind to a 5bet to have to fold and to a C4B to not love that spot either. Leaving aside that villain's strategy is suboptimal, let's focus on our own decision.

In general I tend to take the 'conservative' route and prefer C3B > 4B, in particular because of (1) keeping their weaker hands in instead of getting them to fold and (2) avoiding the akward spot where I have to fold vs 5bet and arrive in a tricky spot when my 4bet is called.
Still, I suspect that even though this might all be true, 4betting still yields a higher EV than Calling the 3bet, by the mere fold equity it receives.

So I took the next situation as my example:

• AKo faced with 3b C-B (RFI 2,5x, 3B 8x, 4B 20x)
  3b stats: 10% B-C
  f4b: 65% B-C
  c4b: 26% B-C (TT,JJ,QQ,AK)
  5bAI: 9% B-C (KK,AA) -> In reality there should be blocker-effects, making this range substantially smaller (like 7% now?)
  C3B or 4B/F?
  (1) EV 4BET (risking 17,5 to win 12 (BB+SB+RFI+3B)
  vil fold: 0,712 = 8,40
  vil 5bAI: 0,09-17,5 =-1,58
  vil c4b: 0,26((x41,5)-17,5) =
  (say x=35, because raw EQ AKo vs TT-QQ,AK = ~45%, and we are OOP so we under-realize significantly..
  .. granted, this seems worst case scenario'ish)
  0,26((0,3541,5)-17,5) =-0,77
  -------
  6,05 (So +6,05bb by 4betting AKo IF (1) villain responds as we assume AND (2) AKo realizes 35% of the pot when flatted

  (2) EV C3B (preflop calling 5,5 to create a postflop-pot of 17,5)
  = 6,05 + 5,5 = 11,55.
  11,55 / 17,5 = 66%
  So, for C3B > 4B, we need to realize 66% of the pot with AKo OOP vs a 10% Button 3B-range.
  (1) vs linear 3b-range, AKo has ~57% 'raw equity'.
  (2) vs polar 3b-range, AKo has ~59% 'raw equity'.
  In both cases, this means we need to realize >100% of our equity, actually somewhere between 110-115.
  Does this seem probable?
  Were I (1) to take blocker effects into account and (2) give AKo a somewhat higher realization% postflop, which might not be unreasonable, we are even forced to realize even more of the pot postflop.
  What is the maximum realization % we expect to have with AKo in this scenario?

What would you do, when faced with this specific spot, being clairvoyant preflop to this particuar strategy of villain?