[khvlgzdv] Large air-supported dome

What limits the maximum size of an air-supported dome, in particular, its height?

The proposed shape is half a geometric mylar balloon.

For a homogenous structure, say, a mountain, the mass increases by the cube (or at least greater than quadratically) of the height, while the surface area of the base increases only quadratically.  This imposes a maximum height of mountains according to the compressive strength of the rock at the base.

However, hollow structures do not have this problem.  Their mass (surface area) increases quadratically, just as the base.  There just remains the problem of distributing the weight of the structure over the entire base, which air-supported structure do.

Rigid structures, e.g., pyramid or geodesic dome, do not work because the weight of a wall increases quadratically, but the wall is supported by its base which only grows linearly.

What is the tension on the material around the base?  Does the strength need to increase without limit for larger structures?  The goal is to build very tall structures for launching things into space without needing superstrong materials like a space elevator.