Stuart Weller was born in the village of Maine in southeastern New York on December 28, 1870. When he was 12 years old, his family moved to Springfield, Missouri. There he became interested in collecting Paleozoic fossils. In 1891, he entered Cornell University, served as museum assistant in paleontology, and completed his undergraduate work in three years. In 1894, he entered Yale, but the following year he was called to the newly organized Department of Geology at the University of Chicago as an assistant to put its fossil collections in order. In 1897, he married Harriet A. Marvin; the couple had three sons, J. Marvin, Chester Marean, and Allen Stuart. Weller received his Ph.D. degree from Yale in 1901 and moved through the various ranks at the University of Chicago to become a full professor in 1915.
Weller's early publications in the 1890s and early 1900s, especially The Classification of the Mississipian Series in 1898, placed him in good stead for assuming additional duties. Shortly after H. Foster Bain took office as the Director of the new Geological Survey on November 1, 1905, he appointed Weller as the first member of his staff. Weller was listed as a geologist, located at the University of Chicago. Weller undertook work for the Survey in paleontology and stratigraphy. He assembled and published the first geological map of Illinois under the new Survey in 1906, a second edition in 1907, and another provisional geological map of Illinois in 1912. In 1914, Weller was the first to detail the Ste. Genevieve fault.
As a result of this work, Weller established the Ste. Genevieve field camp that attracted many students over the years. The camp no longer exists. His efforts in field mapping were focused on the Mississippian System, leading to a large number of mapped quadrangles mainly in Illinois. His son, J. Marvin, who became his field assistant, reported that the early fieldwork was done from tent camps that were moved from time to time by farm wagon. There were no automobiles until 1917.
Stuart Weller passed away unexpectedly from heart failure while in the field in 1927. His work and expertise resulted in major scientific advances for the Survey in geologic mapping and stratigraphic correlations. He was exceptionally influential in the growth and development of the Department of Geology at the University of Chicago and the Illinois State Geological Survey.