That's not high enough to put you above bad weather (airliners fly higher, and they divert around storms.) Bad weather is bad news for airships and historically destroyed about as many as hydrogen fires. You'd need to bring your airships down into hangers when the weather got bad.
Also, wouldn't the graphene aerogel be filled with air and be heavier than air? Aerogel doesn't just float away. Unless you mean for these to be vacuum airships, but those seem very far fetched.
Wow what a fascinating idea! Just thinking out loud here, but the compressive force is proprtional to area, while the boyancy is proportional to volume. So I wonder if making it big enough would allow using some fairly standard materials. What about a cube made of 6 big (huge) sheets of some strong yet light material supported by a sort of skeleton inside?
Or maybe we can use electro-static repulsion to keep it from imploding? Like how a normal balloon compresses the air inside because the rubber tries to shrink but if you had a balloon that tried to expand instead, because of say electric repulsion, or maybe something else, then it would put the air inside at lower than atmospheric pressure.
[1] https://en.wikipedia.org/wiki/Buckling
But regarding your point that the columns would have to scale with volume you might be right about that. I was thinking that it should scale with the total force, but the bigger your structure the longer distance the force has to be transmitted. So yeah I think I got that one wrong.
Only a handful of countries use meters for measuring altitude, and as far as I'm aware they are feeling the pressure to reform to using feet for sake of consistency (read: safety).
Besides, denoting both meters and feet like I did will guarantee everyone will understand one way or another.
If so, I want one.