I'll start with the usual WOW - Best $300 dollars spent! I wish I would have purchased a weber for my first 2.6 13 years ago. Some great write ups on here which helped along the way. Weber with upgraded exhaust makes a world of difference (2.25" piping with high flow cat and FM series 40)

I went with the Holley 1-4psi regulator which I have dialed in nicely right around 2.5psi.

Situation - I wanted to dial this in to the best of my abilities. Knowing one of the most common tools for monitoring carburetor adjustment is a vacuum gauge. When I connected the gauge I was seeing right around 18in-hg of vacuum, and the motor ran well; After spending some time tuning, I was able to get almost 22in-hg - very surprised to be honest, and actually made a noticeable improvement in drivability.

Question - I know the procedure for adjusting via vacuum gauge, but I really want to know how the higher vacuum reading cross talks to A/F ratio. Will the motor idle best at stoichiometric? I guess I really want to know why using the vacuum gauge is such a trusted tool for dialing in your A/F...

I hope that reads pretty clear.

Every engine and cylinder performs different. Many factors are involved e.g. elevation/temp, rpms, timing, fuel, intake and exhaust setup, compression ratio...
An A/F meter would be better for fine tuning.
Stoichiometric mixtures are only used under light load conditions. For acceleration and high load conditions, a richer mixture (lower air/fuel ratio) is used to produce cooler combustion.

The theory is simple.

As to mixture, idle is fairly rich compared to stoich.

It should have no real effect on afr if the idle fuel feed vs. vac is linear. All the fuel feed happens above the throttle plate, and the vac is mostly all downstream from the throttle plate.

The higher the idle speed, the greater the mani vac. Engine speed and thus vac is highest at the optimum idle mixture. You can use a lo range tach the same way.

In either case, you need a tach to set the idle speed. The process is repeated until you narrow down on both the correct idle speed and the correct idle mixture, since they are interdependent. You set the idle speed, adjust the idle mixture toward optimum which raises the idle speed, then reset the idle speed, then reoptimize the mixture. The amount you have to lower the idle gets less and less each iteration until they match (really, when the raised idle from the mixture adj fall in the factory spec idle speed range) and you have it dead nailed.