Just a warning, there’s a lot of *almost* correct but wrong information in this thread, especially in the comments. Orbital mechanics are tricky.
An orbit is stable because the force that pulls you towards earth and the speed that makes you go sideways are ”in balance” with the position. Chance one of them and the others must chance. The counterweight is under tension by the space elevator, so there is an additional force pulling on it. This means that even though it is in a position that would normally be beyond geostationary orbit, the extra force makes it act like it’s orbiting a bigger planet, and thus must go faster.
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