Weideman was born of German ancestry in Detroit, Michigan and attended the public schools.

He attended the Naval Officers Training School at Ann Arbor and enlisted in the United States Navy as an apprentice seaman.

In 1932, Weideman was elected as a Democrat from the Michigan's newly created 14th congressional district to the 73rd Congress, serving from March 4, 1933, to January 3, 1935, in the U.S. House.

During his term in Congress, Weideman was a member of the McCormack-Dickstein Committee, which investigated the Business Plot conspiracy to overthrow President Franklin Delano Roosevelt.

He was elected circuit court commissioner of Wayne County in 1936, 1942, and 1948, and served from January 1, 1937, to April 30, 1950.