Army has always depended on the Air Force for weather support. Army has no weather service.
So if they quit calling it “Air Force” Weather Agency, it would cease to exist.
Actually the Army ran it until after WWII.
“AFWA traces its heritage to the organization of the Meteorological Service of the United States Army Signal Corps during World War I. On 1 July 1937, the Secretary of War transferred responsibility for weather services to the Army Air Corps. United States Army surgeons began recording weather observations regularly in the early 19th century as part of the Army’s medical studies. In 1870, the United States Congress directed the United States Secretary of War to establish a weather service for the nation. Thus, the Army’s first organized military weather service was established in the U.S. Army Signal Corps; however, this service waned after Congress authorized the creation of the U.S. Weather Bureau, today’s National Weather Service, in 1890.
America’s entry into World War I highlighted once again the need for an organized military weather service. Today’s Air Force Weather Agency directly traces its history to the re-emergence of a meteorological section within the U.S. Army Signal Corps in 1917. By the mid-1930s, the Army Air Corps was consuming the majority of the weather data the Signal Corps produced. On 1 July 1937, the Army Air Corps Weather Service, under the leadership of the Chief of the Weather Section in the Office of the Chief of the Army Air Corps, assumed responsibility for all Army weather services from the Signal Corps.
During World War II, the Army Air Forces Weather Service girdled the globe with weather stations.”