" Plan to build a roofed pergola on the balcony of a 2-store house. The plan is attached, removed rails from the schema for visibility. Can't drill the structure or walls. "

Will the roof structure handle the loading? How do you plan to keep this "structure" on the roof without attaching it? Has an engineer looked at this? What about a permit? I cannot see how this is a good idea or will be safe and actually stay on the roof.

by the roof, do you mean the balcony floor? Do you think it can be pushed from the balcony by the wind? As you can see from the photo there are rails

" by the roof, do you mean the balcony floor? "

The balcony is not built for that loading I am sure.

" Do you think it can be pushed from the balcony by the wind? "

100%, deck railing is not stopping that, if it does stop it for even a minute it will topple or it if not thru it.