I've been searching French language sources such as Gallica and French stuff on Google for information on Charles Nicholas Weiss and Jean Gaspard Weiss. I don't understand French but Google Translator is extremely useful.
Anyway, I found this: "Les partitions musicales de Gaspard Weiss retrouvées" - see page 11. It seems that someone else is just as interested in Jean Gaspard Weiss as I am! We'll see what comes of this... I didn't think I'd exhausted the available information on him yet - it would appear that I was right!
November 2011 - Edited to add: Unfortunately this link appears to no longer work. It detailed about a cellist, Tobias Bonz, who had rediscovered the works of Jean Gaspard Weiss. See this post for further details.