Born KY, Benjamin Burch married Isabella F. Pennington 19 November 1818. A history of Washington, MO, places him at New Port, supposedly the first county seat of Franklin County, circa 1819, where he was the architect of the first courthouse. In 1825 an act of Legislature moved the county seat to Union. By 1850, he and his family lived in Osage County, MO, where his wife died in 1854. (an online Washington, MO, history – chap 2)
The sketch of his son below appears to suggest that William S. Burch died in Franklin County. Because his wife was buried in this cemetery, his memorial was placed here.

Daughter, Isabella, married Dr. Leander Rainey. She died in 1908 in Kidsap County, WA.

son Dr. Benjamin F. Burch: Find A Grave Memorial# 14083214

son John Chilton Burch: Find A Grave Memorial# 7117435; http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=7117435
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For additional information, see the biographical sketch of William Burch‘s son, Dr. Benjamin F. Burch:

DR. BENJAMIN F BURCH

Dr. Burch was born in Warren county, Missouri, October 24, 1824. In his early youth he had the advantages ordinary to the country, and secured a fair education. At the age of nineteen he began the study of medicine, and graduated at the University of Virginia in 1845. He began practice in Lynn, Osage county, where he was successfully employed till 1849, when he moved to Washington, where he has been known as a popular physician ever since. Outside of his practice he has been successful as an operator in real estate. He owns one of the finest banks of fire and potters' clay in the western country. This deposit is within the corporate limits of Washington, and was only opened up some six years ago, and it is the source of considerable revenue.

He was married in 1848, the object of his choice being Miss Francis E, the daughter of Judge J. J. McDaniel, of Osage county, a fine personal excellence, and the mother of his four children.

In regard to the doctor's ancestry, we have to record that through the paternal line they reach back to Scotland. His grandfather, Benjamin Burch, a Virginian, was a Revolutionary veteran and an early settler of the celebrated Crab Orchard country of Kentucky. Wm. S., the doctor's father, located in St. Charles county, Missouri, in 1818, and was married to Miss Isabelle F. Pennington, sister of Wm. Pennington, who figured conspicuously as an officer in the war of 1812. From St. Charles he moved to Warren county, and thence to this county. He was an architect and builder by profession, and erected the first court-house built in the county, at Newport; he also built the first court-house in Union, and lived here till his death, which occurred about 1857. He was in all respects an upright gentleman, a strict member of the Presbyterian Church, and was public spirited and enterprising.

One of his surviving sons, J. C, is a resident of San Francisco, where he is known as a leading lawyer, and who represented his district in Congress in the early part of the late war. A daughter, the wife of Dr. Rainey of Lynn, Osage county, is also among the surviving heirs (Franklin County Atlas Page 57)(washingtonmo.com).
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Missouri Marriage Records, 1805-2002
Name: Isabella Pennington
Marriage Date: 19 Nov 1818
Marriage County: St Charles
Spouse Name: William Birch

1850 United States Federal Census
William S Burch
Age: 53
Birth Year: abt 1797
Birthplace: Kentucky
Home in 1850: Crawford, Osage, Missouri
Family Number: 355
Household Members: Name Age
William S Bench 53 [KY][brick layer]
Isabella Bench 54 b [KY]
John C Burch 24 [MO] [lawyer]
William Burch 11 [MO]
Lucy Pennington 60 [NC]

1860 United States Federal Census
Name: Benj F Burch [son of Wm & Isabella Burch]
Age in 1860: 39
Birth Year: abt 1821
Birthplace: Missouri
Home in 1860: Washington, Franklin, Missouri
Post Office: Washington
Benj F Burch 39 [physician]
Francis E Burch 28
Belle Burch 4
Wm C Gordon 16
Wm S Burch 21 [physician]
John Marsh 24
A W Cole 24