vibration at highway speeds

[rh71]

I got my replica 20s on and only when traveling above 60mph on the highway do I notice a vibration. I didn't notice in a week of local driving because I don't take highways much. The vibration is not on the steering wheel, but you can see the passenger seat shaking a bit and definitely feel it in the driver's as well. It is more pronounced if I let off the gas and just cruise.

It feels perfect and non-existant on local roads and anything below 50mph or so.

The tires are still pretty new and have the little tiny pegs that are supposed to wear off. I was hoping this was the cause but it doesn't seem likely and the vibration is pretty bad (seeing the seat shake is not a good sign). I can bring it back to the guys who mounted/balanced it but I'd like to have some idea beforehand. Why does it vibrate only in this scenario? Are those tiny weights (which they've used plenty of) the only solution probably? Is that what's done for balancing?