Actually, the system is balanced even vertically, not just radially. (e.g. if you put the weights on a bicycle wheel
and let it free, it won't move). The error is a common misconception of those who try to make perpetual motion
machines. Just because there are more items on one side than on the other does not mean that the system is not balanced. An equilateral triangle
will not move if mounted on a central pivot
and placed vertically, regardless of the initial orientation.
If you have doubts, do some trigonometry to figure out the component forces exerted by the weights, or try it with a bicycle wheel.
Or, if you like, take a look at the Museum of Unworkable Devices (http://www.lhup.edu/~dsimanek/museum/unwork.htm).
Failing that, build a machine that is inherently unbalanced in any orientation, win the Nobel Prize, the adoration of millions of scantily clad women, and perhaps some self esteem (crucial to your subsequently destined profession as the second coming, being as you will have solved a vast chunk of humanity's problems).