My G-G-G-Grandfather moved to Sumner/Bridgeport Illinois in what was then part of Richland County in around the 1840's.He was a Medical Doctor, but probably treated as many horses as people.Historical clippings from the 1870's described him as an early pioneer of the County and that he cleared and improved farmland for resale.He was a Democrat.
He came from Cinncinati, Ohio.Ohio Census records showed him living there, I think, in 1830 or 1840 census.Directly before him on the census was a John Burgett, with an age that would indicate a father or an uncle.They either lived next to each other or with each other
Before that, all I could find was up in Northern New York State around Germantown Flats before and after the American Revolution.And the early spelling of the name was Burget (one t).My Gdad always said the name was from Alsace-Lorraine, a region of what is now NE France (and heavily German) along the Rhine River Border.But Gdad was always kind of a smart-a**, so I just figured he was trying to cover German roots.He lived through WWI and an extremely anti-German period.I think it was at that time that my family picked up the extra t.
Interestingly, I went to on-line White Page telephone directories for France and Germany.Very few Burgetts, but hundreds of Burgets and heavily concentrated along the Rhine.And most in France.
My brother thinks we are Dutch and the name comes form Burgahardt.But he smokes enough pot to knock down a mule, so I ignore him.I don't think you need a "misspelling" to get a name that still exists in Europe.
In short, I bet on a Germanic/Rhineland origin for the Burget/Burgett name.