His father, Walter Campbell Sweeney Sr., was a United States Army major general and author of the influential Military Intelligence: A New Weapon of War.

Sweeney Junior graduated from the United States Military Academy and was commissioned a second lieutenant of infantry in June 1930.

He commanded a United States Army Air Forces (USAAF) Task Group during the Battle of Midway in June 1942.

In July 1942, he became the air officer for the Theater Group, Operations Division of the War Department General Staff in Washington, D.C. [citation needed] In July 1944, Sweeney was assigned to the 73rd Bomb Wing and moved with this unit from Colorado Springs, Colorado, to the Pacific area, serving as chief of staff and later deputy commander.

In July 1945, he became director of plans of the Strategic Air Force, Pacific Ocean Area, Guam.