1973 Dodge Dart sport speed related shimmy

I no longer have nor have ever had the original wheels and tires. It seems just recently if I even run a sustained speed starting anywhere from 45 miles on up it starts to occur now. The steering is not effected until the shaking becomes more pronounced, then you can feel it pretty much throughout the whole car. Drums still have their weights on them too. Tires and wheels are all new and this started before the new wheels and tires were installed. The wheels and tires I replaced have since been sold but they were centerline wheels and not oem.