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does it not matter? Some like to fix them to the inner side of the wheel for a cleaner look. That's fine, but not important. Please, there are engineers, experienced, licensed mechanics, and longtime tire/wheel specialists visiting this fine forum. Let me hear from you, not one of the guys who lives here and feels a need to chime in on everything.
Thank you for any vetted insight, corroborated knowledge.

For the very best results, weights are placed, as needed, on the inner or outer side, or both. Good luck finding a credentialed engineer to balance your wheels and publish a paper on the job.

I am an aerospace engineer who has built many spin stabilized satellites (same as spin balancing wheels). I hope you don’t slap me down because I’m a regular on the forum.

There are two types of rotational balance:

1) Static Balance: this is what you do to get the center of mass (aka “gravity”) of the wheel centered back onto the spin axis (axle) as well as between the inner & outer hub. This is what a conventional “bubble” wheel balancer achieves. Unfortunately, many mechanics mistake this for total wheel balance and are puzzled when they still have “wobble” at speed.

2) Dynamic Balance: without going into the math, the physics of a perfect spinning system seeks a symmetric mass of all points, both in the radial and inner-to-outer direction (along the axle). Small irregularities in the wheel, spindle, tire fabrication, even paint/hubcaps cause slight asymmetry that results in imbalance and “nutation” (difference between the desired geometric axes and the actual off-nominal mass “principal” axes); this is often what causes the wobble in a kids spinning top or a yo-yo. A rotating spin balance adjustment (wheel balancer) applies small weights to two “remote planes” (the two hub rims, inner and outer) to bring this principal mass axis back into alignment with the forced spinning geometric axis (axle).

To get at your question: the lowest mass balance weights used and the quickest balance solution is achieved using BOTH inner and outer hub rims to attach balance weights to. It may take up to 10 times the masses and balance time to do the same task using just the inner hub to attach the balance weights, so your mechanic might not be willing to go down this road for a fixed price. There is a moderate probability that they can’t converge on a “single plane” solution and need to use both hub rims anyway.

Frankly, let the simplest solution be used with both inner and outer hubs; it’s what the spin balance machine “math” is set up for and just paint the balance weights afterwards.

I have a bachelor's degree in mechanical engineering, cum laude and with Honors, and I took a graduate course in in dynamic and Lagrangian mechanics while an undergrad.

Here is a useful graphic showing why they are both important. It's critical to conceptualize that this graphic is not showing physical runouts but instead runouts of mass distribution. (Obviously a physical runout of something of a constant density will also cause a runout with regards to mass, but physical runout on a tire causes other problems independent of wheel balance. Commonly called a bumpy or out-of-round wheel, and pretty rare nowadays when using rims and tires from reputable manufacturers.)

For static balance, the wheel will (theoretically) roll on its own when suspended in the air so that the center of gravity ends up below the axis of rotation. (In reality, the difference is often small enough that the wheel is rotated by a motor and the imbalance is measured by sensors.)

For example, when driving, at the instant during rotation of the wheel while the imbalance is up, the wheel will deflect towards the car, slightly compressing the suspension and making the car drop very slightly. After the wheel rotates another half turn, the effect is reversed, noticeable as a wobble.

Dynamic balance is easiest to understand through this thought experiment:
Picture two wheels that are half the width of a normal wheel but mounted together. Each half-wheel is out of static balance, but each is imbalanced by the same amount and the imbalance is positioned in the opposite direction for each. So while while the pair of half-wheels as an assembly will have correct static balance and not spin on its own, the wheel will want to wobble for the same reason that a wheel out of static imbalance will want to wobble, it will just wobble differently, but it is a problem just the same.

For example, when driving, at the instant during rotation of the wheel while the outer half of the wheel is imbalanced up, the inner side is imbalanced down, causing the wheel to deflect in the direction of negative camber, and again noticeable as a wobble.

Therefore, it is necessary to have both a correct static and dynamic balance.

I'm pretty sure you could balance a wheel using only inner weights and centralized weights. If you only have inner and outer weights though, you will have to have a bunch of wheels to try out to avoid using outer weights.

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For most Packards running stock or near-stock tires at legal speeds, you can do an adequate balancing job with a good bubble balancer. This assumes the tires are OK and the wheels are good. Most tires today are mounted with power equipment and balanced on computerized "spin balancers". A good operator can do a good job with this equipment, if it is in good working order and the wheels and tires are in good condition. Brake drum balance can be a problem in some cases, as can bent axles and loose parts. Some tires have stiff areas or other defects that will cause issues. Poor shock absorber function or loose shock linkage will cause problems. Stick-on wheel weights can be an alternative to conventional rim weights where appearance or wheel cover fit are issues. I don't know if there are any specs for allowable wheel run-out. Some vehicles have "lug-centric" hubs and some have "hub-centric" hubs. Using the wrong wheel for the hub on the vehicle can cause run-out issues.

At one time, offset lead balance weights were available for use with full wheels covers or trim rings where the standard wheel weights interfered with the cover or ring. These had an extended clip that moved the weight inward a half inch or so to allow the wheel cover or trim ring to lie flat against the wheel's outer rim.

My brother has a computerized Hunter Coats not sure of brand but balance machine made in usa. Which can spin balance wheels and tire and will place weights where you want them like on flange or inside near bead. All you need to do is during setup indicate where you want weights placed. This allows weights can be kept off of outside on designer wheels such as chromer wire.