[Gurkenglas]

If the capacity is proportional to the depth of the tunnel and the mass of the weights, and the maximal mass of the weights is proportional to the depth of the tunnel, then wouldn't the capacity grow quadratically with the invested money?

Edit: You assumed that they can both fill most of the tunnel up with lead and move that up or down 500 meters. The volume that they can fill with that is thus only half of what you say.

[msandford]

Why is the maximal mass of weights proportional to depth? It's more proportional to diameter than anything else. There's a practical limit to how much weight you can hang. Sure if you make a 10km deep hole and a 3km deep weight you could store a lot of energy. But a 3km deep weight might not hold itself together.

[Gurkenglas]

If we have enough volume that we can't use the most dense possible weight for all of it, we can find cheaper weight materials by dropping the density constraint.

Couldn't you have the weight grip the sides of the tunnel with gears attached to a generator/motor (inside the weight) so the weight wouldn't rip itself apart? It would be the same machinery that ordinarily would operate the pulley at the top, just moved down into the weights (cause with this, you would need no more pulley). (To illustrate why it wouldn't rip itself apart, imagine gaps on the weight every 100 meters.)