According to Wikipedia:

Gordon Hill Jenkins (May 12, 1910 – May 1, 1984) was an American arranger, composer, and pianist who was influential in popular music in the 1940s and 1950s. Jenkins worked with The Andrews Sisters, Johnny Cash, The Weavers, Frank Sinatra, Louis Armstrong, Judy Garland, Nat King Cole, Billie Holiday, Harry Nilsson, Peggy Lee and Ella Fitzgerald.

I think Jenkins was responsible for the "big band" sound of the earliest Weavers recordings.