This whole posting is due to someone not wanting to see the weight on the outside of the wheel. Not because they don't want it balanced.
Like balancing a crankshaft, you put the weight where it is needed not where you want it. No matter how "good " you are, you can't change the law of physics only try to fool it. Remember that garbage in garbage out. Lie to the balancing machine and it will just lie back to you.
Look at an OEM restoration and the weights will be on both sides of the wheel. Look at any high performance car, race car and you will see the weights.
Problem . To properly balance a tire, the weights must be on opposite sides of the wheel. This is called dynamic balancing. The wheel will want to do 2 things when spinning.
#1 Static imbalance, the wheel wants to hop opposite the heavy end of the tire/wheel.
#2 Dynamic imbalance, the wheel wants to wobble due to side imbalance.
Remember that until the electronic balancers became common in the early seventies, balancing was done with a bubble balancer. If you are younger than 40-50 you probably don't even know what that is. It was what it sounds like, using a leveling bubble to equalize the weight when laying the tire flat. Very crude but remember that the suspension systems were relatively crude, tires and wheels were narrow and most driving was done at lower speeds. High speed balancing was generally done on the car. This took experienced people to do and was very dangerous.
I got my start in the tire business back in 69-70 just when wider tires were becoming more available. Before then, guys would use old racing tires on the streets to get the wide look. Not DOT rated and didn't last very long at all. A lot of s/w failures.
Just tell the tire shop that you want the tires balanced properly and see what happens then. Not,"can you balance them with all the weights on the back ?" If you do that, your wheel will look like the one in the picture. Look closely and you will see that the weights are on the outer edge of the rim on one side and the inner edge of the rim on the other. Not really operator error, just trying to do it by not telling the balancing machine the proper information and the balancing machine trying do something that is based on false information.
https://r.search.yahoo.com/_ylt=Awr9LvCl1VNfMY0AmwEPxQt.;_ylu=Y29sbwNncTEEcG9zAzEEdnRpZAMEc2VjA3Ny/RV=2/RE=1599358501/RO=10/RU=https://e-quipfix.co.uk/wheel-balancing-101-static-vs-dynamic-wheel-balancing//RK=2/RS=Z9bjyjwfhlc4pf.Euzn75a_MhyI-