about a space elevator

I would like to ask you guys about something that I can't grap... If we design a space elevator, based on earth stretching until the GEO with tether elements and if we use a counter balance (let's say an asteroid) around 47 000km above the earth ( at the escape height) the center of gravity will be located in GEO point... but the asteroid will travel with less speed although it is located as a counterbalance.... how does this counterbalance work properly?? best anilir