4betting there doesn't seem very good if we think his range is largely air, right? What are the likely outcomes when we 4bet: He folds basically all his air, 5bets his nutted hands with plan to GII, and calls with... what? He's likely quite polarized here, so what are you realistically wanting to have happen when you 4bet? It seems like you are looking for a call from a range you're ahead of, ie getting value, but I think a call is the least likely thing for him to do and he may not even have a call 4bet range in this spot at all.
Typically if we 4bet someone who is unlikely to call, and folding or gii are both -EV then we screwed up with the 4bet, cause it means the 4bet was -EV to begin with. (Granted, there is dead money to pick up, so it could still be +EV, but it will be more marginal if all we want him to do is call or fold. Plus if you think he's squeezing here a ton then pick a different type of hand to 4bet here -> don't waste AK.)
