Peter Gray – I agree with JT.
It appears that the ground floor occupant has placed items on the common that are not permanently installed, therefore it is unlikely that the ground floor occupant is claiming the area as their Exclusive Use. Also, there appears to have been no permanent barrier erected around the area that ‘excludes’ others from entry to this area.
The usage of an area, even on a continuing basis and for a long period of time, is not sufficient to acquire exclusive use rights.
Occupants are permitted to use Common Property. Whether they elect to make use of the Common Property or not is their own personal choice.
Unless there is a By-law restricting BBQs, BBQ smoke may drift from BBQs on balconies just as readily as it does from the Common Property lawn area.
You may have the benefit of a view being that you are on a higher floor, and the ground floor occupant has the benefit of easy access to the garden. C’est la vie!
If the occupant is creating excessive noise then you may be able to invoke the ‘noise’ by-law. Apart from that I don’t see that you have many other avenues of complaint.