There are several aspects to tire balance. The two main ones are radial imbalance and lateral imbalance. Radial imbalance gives you the shakes. Lateral imbalance gives you the side to side shimmy. You are more likely to have a lateral imbalance if you have wheels that won't properly center on the sheel and/or balancer. You are also likely to have lateral imbalance if you try to balance on a single plane with stick on weights. It is best for balance to use weights on the inside AND on the outside. A belt that is out of position can also give you a problem with lateral balance.
I would say to have a good hard look at the balance before doing anything else.
