[RightWhale]

The force pulling up on the anchor

That is correct. The entire structure would be in tension, so the heavier the structure and elevators [assuming multiple elevators so they can lift enough cargo to make it worthwhile] the greater the tug on the anchor. You'd eventually want something the weight of the Cheops pyramid at the ground end.

[PatrickHenry]

You'd eventually want something the weight of the Cheops pyramid at the ground end.

I wish you hadn't said that. Now the crazies will come into the thread claiming that the pyramids were ancient anchor points for Egyptian space elevators.

[Brett66]

The elevator they're proposing is designed for payloads of twenty tons or less. How many tons of tension on the cable would that require? By the looks of the size of that platform, it might come close to the weight of a pyramid.