Let's assume a desired maximum payload height of 22,000 miles and maximum weight/mass of 100 tons. That means we'll need a pulley at 44,000 miles supporting both the payload and the 100 ton counterweight.
The ribbon extends to 62,000 miles. Place a weight/mass there such that the centripetal force equals 200 tons plus the weight/mass of the ribbon. You could now disconnect the ribbon from the ground.
The rising payload will need to be accelerated horizontally and the descending counterweight decelerated. Lots of wasted energy.
"The system must remain in equilibrium, once set up. This means a counterweight to the payload."
Not really - there's no reason you can't add more mass to the system. The energy to acclerate the payload horizontally as it climbs comes, in the end, from the earth's angular momentum - every bit of mass we send up the space elevator will steal of bit of the earth's momentum. I suspect we would have to send a significant amount of the earth's mass up it before it would affect the angular velocity of the earth's rotation, though, and given how massive the earth is I don't think that's likely to be a problem.
C'mon, guys, some very smart people have figured this out and can show that it is workable, at least in theory. I think we can take their word on that part, at least.