I was going to make a long post, but it was a wall of text. Here is the easy fix.
Hire a carpenter. He will come out, and either
A. level the floor under the tank.
B. fix a defect in the stand where one leg is too long, short, or warped.
C. Tell you it is already balanced and level, the problem is weight distribution cause by poor design of the tank itself compressing the carpet mat with very different degrees of pressure, a defect or poor design who knows. (in this case try a Mat specially made for this situation they sell for aquariums they cost 20 bucks, and fit between stand and the tank. it will help balance the tank.
D. Nothing worked. Return it and get a new tank
Oh 1 more thing. NEVER use shims on balancing that much weight on carpet. You may by some miracle get it to not wobble, but the pressures will be WAY off and could cause stress fracture of tank or the stand. If you have a 3 inch shim, you are placing ALL of that weight on a very small surface area. In addition if this issue is cause by WARPED wood, the integrity is already compromised. Hopefully it is just bad sanding at the factory.
I know very little about fishtanks, but I did get a B+ in physics at a community college. Oh and I was a combat engineer in the army.
