Seems to me that "reçoit la bourgeoise de Steffisbourg" must mean that the family was granted citizenship in the town... "with all the rights and privileges pertaining thereto."

But, I'm just guessing, so far.

--------------------------------------------------
Note added at 22 mins (2009-06-11 13:53:16 GMT)
--------------------------------------------------

My thought is that "bourgeoise" here means more that just some vague "class" designation --it had a more specific, juridical meaning (here, according to the "Law of 1799").

So being granted citizenship in a town ("reçoit la bourgeoise de..." = "was granted the title of citizen of...") was something more than just a family coming from somewhere else and moving in to a house within its walls.

Though I can't find a phrase exactly like this in the TLF, here's part of its definition of "bourgeois":

1. Libre habitant d'une ville, **jouissant de certains privilèges**...

P. ext.

a) Citoyen d'une ville. Des riches et honorables bourgeois.

b) **Helvétisme**. Personne qui possède le droit de cité communal. Une commune ne traite pas toujours identiquement ses bourgeois et les autres citoyens du canton (J.-F. AUBERT, Traité de dr. constitutionnel suisse, Neuchâtel, t. 1, 1967, p. 371).

2. Ils [les compagnons Imprimeurs] aimaient à se faire **donner le titre de bourgeois de Paris**, dont ils se distinguaient peu d'ailleurs en public par leur mise toujours soignée.

http://atilf.atilf.fr/dendien/scripts/tlfiv5/affart.exe?19;s...

From 1. b) it appears that the term among, the Swiss in particular, implied considerable special juridical rights and privileges.