Can you solve the burning stick riddle? ft Simone Giertz part 3/3

I think I just invented the space funicular, if noone already did. It's like a poor mans version of the space elevator, and it reaches only the stratosphere or so, not geostationary orbit. A platform is lifted to great height, using baloons. Aboard the platform is a heavy counterweight, attached to a cable. The other end of the cable reaches down to the ground and is attached to the nose of a rocket. At launch, the weight falls down, accelerating the rocket upwards. The aerodynamic weight is heavier than the rocket, by a suitable amount. When they inevitably meet about half way, they must somehow not get too close. Later, close to the platform, but again not too close, the rocket detaches from the cable, and maybe ignites a conventional rocket stage for its continued journey. Apart from the danger of internal collision, the mass of the cable will gain a significant momentum. This momentum somehow switches its direction from up to down, near the platform. If that doesn't work flawlessly, there will be trouble. It'll mess up, won't it? One does not simply run a cable car at rocket speed?