[John Jamieson]

Just HOW does it do that?

You can't just pullup a payload without throwing yourself out of obit. The payload has to be boosted up the line, same as it would be without the line.

Now if you happen to have an infinite supply of mass already at the top end, you can send down the same amount as your pulling up and remain stable.

There ain't no free lunch (or launch, either).

[John Locke]

Not a hard problem. You have to conserve not mass but angular momentum. So you can balance a lot of payload merely by moving a counterweight outwards along the tether.

When you run out of tether, drop mass back to Earth and you can reset the counterweight.

So, we need a regular supply of mass at the top of the tether. Fire it off the Moon with a magnetic railgun, again at very low cost (about 15 cents per kg in raw energy - yes, energetically high Earth orbit is much, much closer to the Moon).