A Google search turned up a county genealogical group. This might be a help to uncover additional information. You might want to contact them. They have among other resources, the following info->
U S Census for Charlevoix County - 1870, 1880, 1900. 1910. 1920.
My Thayer line ended about 1700 in MA with Margaret Thayer.
A description of the origin of the Thyer surname is available at www.surnamedb.comas follows:
Last name: Thyer The famous victorian etymologist Canon C.W Bardsley considered this surname to be a medieval nickname form of the Old French personal name "Thierry" - the modern Terry. Subsequent attempts to establish an alternative origin have failed, although the appearance would certainly suggest that a locational origin may be possible. The Olde English word for a ancient pagan God was "Tiw" also recorded as "Tyw", and this spelling plus the suffix "er" would indicate a person who lived by the place of the ancient gods - a temple. However this is an unproven conjecture, which will remain unproven until additional "Thyer" records are discovered. One of the many curious features of this name is that even as late as the 19th century variant forms were still appearing. Examples of the spellings include Giles Thyer, a witness at the christening of his daughter Elizabeth, on October 6th 1667, at St. Botolphs without Aldgate, London, and Frances Thyer, who married John Hawes on September 30th 1788 at St. Martins in the Field Westminster. On August 21st 1847 Robert Thirs was christened at St. Pancras, and on March 6th 1862, Thomas Thyers, a patronymic spelling, was christened at the same church. The first recorded spelling of the family name is shown to be that of Antony Thayer, which was dated July 15th 1605, married Martha Bourman by Civil Licence, in London, during the reign of King James 1 of England and V1 of Scotland, 1603 - 1625. Surnames became necessary when governments introduced personal taxation. In England this was known as Poll Tax. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.