Unfortunately, as l1tech said, there are a lot of idiots who cannot properly balance tires. They don't look for tire problems balancing...If he machine says the tires are balance, that's good enough for them.
As I previously said, it is possible for and idiot to balance tires that are out of round and they wil balance, but they will cause the vehicle to bounce and vibrate when driven. I used to have that problem with and old Buick Regal I had.
Also, what Eddie said is also very true. When you see a lot of balancing weight in on tire it is often caused by the heaviest part of the tire being mounted on the heaviest side of the wheel. That makes it harder to balance and those idiots will just stick more weights on. They often will not take the time to break the bead, shift the tire 180 degrees, reinflate and then rebalance the tire. I think this a more common problem with alloy wheels when they use the clip-on wheel weights. Alloy wheels don't have the deep lip on the edge of the rim to hold the weights and too much weight in one location can cause centrifical force to throw off the wheel weigts at speed.
By all means, go to another shop and explain your problem and what you have had done. They will probably want to rebalance your tires, which is fine, but also have check to insure that you do not have defective tires, or bent rims.
In essence, don't tell them what to do..ie: Balance my tires, etc. Tell them them you have a vibration problem and what you have done so far to correct the problem, but insist that they diagnose the vibration problem and you want the problem fixed. They should not to just assume anything. You may have to pay extra for the diagnostic services, but If they say it's a wheel balace problem, tell them that if that does not solve the problem, then you will not pay for an unneeded wheel balancing. A good reputable shop will not balk at that. You should only have to pay for the correct diagnosis and repair of that problem and not for them to randomly throw parts at the probem.
I personally think you have a bad balance job. That could be caused by the heaviest part of the tire mounted on the same side as the heaviest part of the wheel, or it could be caused by one or more defective tires/wheels. But nobody here can diagnose your problem with 100% accuracy without seeing and testing the vehicle. They are all just possibilities, and might be a common problem it could just be a lucky guess. Your vehicle may have a different issue and your discription may be misleading. That's why properly diagnosing the problem is the first step and overall, the cheapest path to getting the problem resolved and not speding money chasing ghosts.
If you cannot diagnose these problems yourself, you a better off just going to a competent shop, and explaining the problem in detail, and pay them to diagnose and repair the problem. In the long run it is often cheaper.
...Rich
