Probably depend greatly on what you wanted to do with the extension. If you just want sun and weather protection a hard-top extension could be made pretty lightly. But it seems a shame to have that space and not be able to use it for anything other than a cover, so making it strong enough to hold stuff or people or both would probably come with a not-insubstantial weight price. To the point where I'd start thinking about getting some stability data, particularly if I intended to use the extension for stowage containers, a dinghy, etc.
On the other hand, if one is adding a strong hard top extension to a boat that already has a version with such an extension installed by the manufacturer, a stability study may not be important. For example several models of Grand Banks were available in tri-cabin, sedan, and Europa configurations. All using the same hull, same basic cabin dimensions and construction, engines, tanks, etc. So if one had a GB36 Sedan and wanted to add a hardtop extension over the aft deck strong enough to carry a dinghy on, you'd be doing what the factory already did to create the GB36 Europa.
