Bought the tires online, great Michelin's - and no-one can balance them right. There's been a shudder as my speed increases since I got them put on.

Finally took them to the dealer today. They seem to have fixed it, though it's annoying that the weights are on the outside of the rim, and it still feels a little funny intermittently around 80mph.

 

If the wheels only had weights on the inside edge of the rim then they were not balanced as well as they should have been. A proper balance needs a balance set up to be able to have weights on the inside and outside of the rim. Anything else is a compromise.

 

Correct! To many service techs think they are doing you a favor by placing the wheel weights behind the rim so as not to distract from your brand new tires and shiny rims. This is known as "Static balance". It's nice when it all works that way.
More often than not what is needed is a "Dynamic balance". The dynamic balance is more precise at placing the weight where it is needed for that smooth ride.