How is 'Burget' spelled?

This family usually used the name Burget, or Burgett, in the 20th C. But it has been spelled differently by different authors at different times for different reasons. It seems likely these referred to the same people.

1776 - Charles A. Fisher's Early Pennsylvania Births 1675-1875 said that Martin Bugart & wife had a son, Emanuel, on 7/1/1776 who was baptized at the Himmell Lutheran Church. The church was in the southern part of Northumberland Co. Pa. and the records were kept in German. 

Burkhardt. Bergit, and Birgit appear in the 1791 records...

"...A small detachment of United States troops, under the command of Lieutenant Kingsbury, occupied the fort. It consisted of a corporal and eleven men, besides the commandant. Their names were Taylor, Neef, O'Neal, O'Leary, Lincoln, Grant, Strong, Sowers, Murphy, Abel, McVicar and Wiseman. There were on the north side of the fort, Horn, McDonald, Barrott and Barket, with their families, and on the south side, White, with his family, and McDonald, whose family was not at the station..."

1792...

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"A Collection of Pioneer Marriage Records, Hamilton Co, Ohio 1789-1817 - Vol. 1 shows a marriage between Betsey Burget "'widow of Colerain'. One Martin Burget, Colerain, dec. prior to June 1794."
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"The Hamilton Co. Probate records for June 14, 1794 indicate that "Letters of adm granted to John DAVIS of Colerain, Yeoman on the estate of Martin BURGET decd. Bond $300. Sec Mary HORN." "Jan.6,1795. Martin BURGET decd. Inventory and appraisement of John DAVIS, admr, allowed. 

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BsS...

On 18 Feb 1926, Jean was described as a Burgett

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