Ok, now this is getting too weird. Don't take this the wrong way, but it seems apparent you know very little about auto mechanicals, and tire/wheel mechanics in particular. When a shop balances, or re-balances a tire, it is normal to remove all existing weights first. A tech could try leaving the existing weights on, and spin the tire to see if there is a balance problem, but if the balance machine indicates a problem, then it will indicate where and how much weight is to be added to balance the tire. At that point, it doesn't make sense to add additional weights to what is already there to acheive proper balance. It makes more sense to remove all existing weights, start from scratch, and add only the amount of weight necessary to balance the tire. This is why I first suggested that if you are NOT experiencing any tire vibration, having the tires re-balanced doesn't make sense (IMHO).
They didn't remove the weights to screw you. It is normal proceedure