Is there anywhere to read about the physics of this for a mechanical dummy? Specifically I'm wondering, wouldn't the counterweight be pulled toward earth every

Is there anywhere to read about the physics of this for a mechanical dummy? Specifically I'm wondering, wouldn't the counterweight be pulled toward earth every time we use the elevator? Would we have to continually boost it? Does the counterweight have to be in a geosync orbit, or the center of mass? If the latter, what keeps the counter weight in geosync?