Hi Sally,
Sorry it has taken a while to get back to you but I had to check a few things with my sister (who has tracked that side of the family).
Your William Beaumont Buer we think is the grandson of William Buer bapt. 23 Nov 1783 Covent Garden, Westminster, London - d. 1841 (married to Francis Knill.) This William was a butcher.
I think your William Beaumont's father also William Buer, went on to become a Pawnbroker and his decendants then went on to make some serious money.
William Beaumont's great-grandfather was my ancester William Buer b. 1749 - d.1829. He was also a butcher, but came to own a lot of property and became before his death a "Gentleman". The family heralds from Great Parndon, in Essex, where we think his father Joseph Buer was a simple farmworker (although we have no hard evidence) however his son William was made an apprentice (belonging to the Merchant Taylors) which set him on the road to self improvement.
We have quite a bit of information (i.e. detail on the above)and on the family which we would be happy to share.
Regards
Max