This sounds oddly similar to parts of Tomás Saraceno's "Aerocene" art initiative. Heck, he's literally written a book about the subject:
The general idea of that art project is to have solar-powered hot air balloons, where the amount of buoyancy is not bound by the gas volume, but rather by the amount of solar energy that can be captured - making the structures spread horizontally, and in a organic way, creating a web of connected aerostatic polyhedra (pretty much like a cloud of connected soap bubbles), as depicted:
This concept of "cloud city" aligns with your premises, i.e. it would grow organically as more people attach their balloons to it. It doesn't need any kind of regular structure, since a web-like construction should spread the tensile load around just as well as a regular grid, and connections don't need to be standard, but rather the sheet material should be easily movable around.
Now, what you don't want in a structure like this is rigidity. You want the structure to be flexible instead (and elastic), since it will be able to withstand hazards much better. Just like buildings in an earthquake shake table, suspension road bridges under load, or airplane wings being bent.
Also, since growth is supposed to be organic, I don't think such a city would create a central larger structure. If there's plenty of spare room at the sides, and buoyancy would suffer by vertical growth (making vertical expansion more expensive), why would people want to build that way?
After all, we already have organically-growing cities floating in a fluid, and they look pretty flat:
Now, keep in mind the economic principles why expansion happens that way - expanding horizontally is way cheaper, and it's organic and chaotic due to lack of regulation.
With this kind of cloud cities in mind, I cannot come up with a reason why the denizens would want to build a bigger (higher/deeper) structure in the middle. I can only think of large-scale exotic approaches, such as NGOs or corporations (or a massive government/community effort) installing a huge buoyant structure in the middle (a cloud-9 geodetic sphere as suggested in other answer?), which would prompt the connection of non-buoyant structures underneath.