I bought wire wheels from Coker for my '64 TBird four years ago, pre-mounted and balanced and one of them had about 8 adhesive wheel weights on it while the others only required one or two. I took it to my tire guy who removed the tire, remounted it 180 degrees off and found that it required the same number of weights, so it's the wheel not the tire.

The car ran smooth at highway speeds until recently. Some of the weights on the "bad" wheel fell off so the assembly is again out-of-balance...

"Permanent" wheel weights?