[nickff]

Gravity does decrease quadratically, but the origin is the center of the earth, not the cable's anchor. The earth's diameter is over 12000 km, so gravity would not decrease significantly over the 10s of kilometers the balloons supported.

[tinco]

Argh you are right at 160km it's only dropped about 10%. It's a tough world out there :(

[JabavuAdams]

Well, to be fair to an otherwise impractical idea, getting up above the dense part of the atmosphere helps.

If you're trying to get to space quickly, then much of the air-resistance losses are in the first 10 km.

Look up "rockoons" for more info on replacing a rocket's first stage with a balloon platform.