What kind of restrictions are there on airspace use for such project? Airspace might be the wrong word. Is there a chance an aircraft might hit the ballon etc?
Coutry/state regulations vary across the world. Almost everywhere (might be a place on earth where this isn't legislated) you have to get proper authorization with a civil aviation agency.
In Germany, you need a permit from the authorities (in this case: Regierungspräsidium Freiburg, cost: 30€) and you have to register a weather ballon launch at the German flight control (Deutsche Flugsicherung, cost: free).
https://ukhas.org.uk/guides:faq