Variance or not to variance, that is the question

there is no way you can fold to a max $150 shove, so bring the money in by yourself and at least realize all your equity

What was the purpose of 4! with AKo to an amount less than a shove?

How do you know that this guy was 3betting with a range that you are ahead of? In my experience when a player who is normally passive 3bets, it’s time to watch out.

Given that your read is correct, I would almost rather fold preflop than 4bet to this size. Even if you are usually ahead of V1, that sizing is really laying odds that you haven’t run into a huge hand from him. And if in fact you don’t care, then just jam yourself.

Grunch:

What do we make of V1's min-click 3B sizing here? Is that an indication he wants action, or a sign of weakness, or just a pot juicer?

The stack sizes are awkward for a 4B. Think I'd either flat call, or jam pre, not 4B for this huge size that commits us post-flop. If we think our opponents are going to fold, I'd jam. If not, I'd flat.

As played, we're not folding, obviously. Think we can just get it in. Hopefully they both fold, even getting insanely good odds to call with any pair and any draw.

Get it in and hope you have ten outs when called.

There's $120 in the pot when it gets back to you and 3 people in (worst player IP, the rest you are OOP). So you can fold; call $20; or raise ... If you are going to raise I think the only sane size is all of it.
Even a min. raise to $55 total (assume everyone calls) means you are going to see a flop with less than 1 SPR against most of the players, and less than 2 SPR vs. V1. Going bigger just makes the SPR problems worse.

Eg. As played on this flop, if V1 shoves and turns over QQ before you act then I think it's very close to 0 EV to call. So just auto shove and hope to run good.

Preflop seems like a fairly straightforward 4bet jam. This sizing is just a bit of a mess given you're committed pretty much whatever happens.

You now might just have a sliver of fold equity against some hands which you're behind/chopping with, so the right play now is to jam. You're not going to get anyone with less equity than you to jam, so do it yourself.

Result:

With all the dead money in there? Seriously? Not to mention V1 3bet range has already been defined to include hands like 77 and AJo. It's an absolute slam dunk 4bet and the only real debate is on the sizing (which seems to me that all in is the only logical answer, but at least there could be some sort of argument for something else)

His 3-betting range here is like 88+, ATo+, A9s+, KTs+, QJs. We have a lot of hours together. His 4-bet calling/continuing range is like AQs+ JJ+ AKo.

That may be true, but when we 4B to $250 over his $35 3B - and he calls - he's going to be weighted more towards the better part of his 3B'ing range.

If you want to 4B here, you could make it $100 to $130. That puts a ton of pressure on V, but still doesn't pot commit us.

ETA - I asked what his small 3B size indicated. Oftentimes, when someone is 3B'ing wide, and they know we know it, they'll size down with a strong hand, hoping to induce a 4B.

If he is 3b wide like you said, then just jam pre. I guess just rip flop as played.

Note, you said he 3b with AJo and 77. This isn't super useful information by itself. Those hands are okay to 3b facing a raise from certain players in certain positions. The question is, is he positionally aware? Is he doing this on the button vs the cutoff? Then doesn't tell you a ton, he might just have a decent preflop game. If he is 3betting UTG + 1 vs UTG with AJo then yeah he is ultra wide and a shove is probably winning here.

Easy 4bet. I wouldn't go all in because I think that will be interpreted as trying to take it down now. The average player is not going to like 10x it here with AA. 250 is ok. I might go just a bit smaller. AP, go all in and maybe once a decade they fold 88 and 99 and you beat the guy who just has random stuff, and otherwise hope to hit.