There is a Peter Baier who came to the US in 1872. He was a naturalized citizen in 1900 in Bruce Township, in Macomb Co MI. His wife, a MI native of German parentage was named Mary. He had two daughters, Jeannie, Mamie and a son named Stuart, Stewart. The census form is difficult to read.
In 1910 I found a Peter Baier who lives with his wife Mary, son Herbet, daughter, Mae. He was a blacksmith. He was also a naturalized citizen who arrive in 1871.
I believe there is some chance that this is the same family as the age of the adult children seem to be consistent.
Hope this is the helps.