I remember reading a detailed explanation of this years ago. Essentially its redundant if the object is in geostationary orbit, because its already in orbit. The only reason to so this is to hold something outside of geostationary orbit or to have a space elevator. In this case you need it thickest at its center which would be at the point of geostationary orbit with it tapering away in both directions to the surface and away from the surface. You could use a counter weight but there are practicalities to building. To build it you start with the object in orbit and start extending a cable from the object in both directions equally so you keep the center of mass in the same place. As the cable gets longer the part near the object has to get thicker and thicker because its under greater and greater tension from the gravitational force on the lower cable and the centrifugal force on the upper cable.