Born in Baltimore, Maryland, Stockbridge attended public and private schools and Williston Academy of Easthampton, Massachusetts.
He graduated from Amherst College in 1877, where he was a member of Chi Phi fraternity.
Stockbridge was elected judge of the supreme bench of Baltimore in November 1896 and served until 1911, and was a Regent of the University of Maryland from 1907 to 1920.
He was appointed judge of the Maryland Court of Appeals on April 13, 1911, and was elected in November 1911 for a term of fifteen years.
This article incorporates public domain material from the Biographical Directory of the United States Congress