Born on November 16, 1905 in West Hoboken, New Jersey, he was the son of Washington Weaver and Jennie Weldon. A blood brother, Father Bertrand Weaver also became a Passionist priest. Father Alfred Weaver’s maternal grandfather, Patrick Moreland Weldon spoke at the dedication of St. Michael’s Monastery, West Hoboken in 1864. Father Weaver took his Passionist vows on September 12, 1926. He was ordained a priest by Bishop Thomas Walsh of Newark, New Jersey on May 22, 1932.
Father Weaver was first assigned to train Passionist seminarians. Then from 1941 to 1944 he was Assistant Superior at St. Ann’s Monastery, Scranton, Pennsylvania. In 1947 to 1960 he returned to Scranton as pastor of St. Ann’s Parish. He gained respect for his organizational abilities. He established a parish credit union. In 1960 he was appointed pastor of St. Michael’s parish in Union City, New Jersey. From 1967 to 1973 he served as a hospital chaplain in Baltimore, Maryland. Just prior to his death his was residing in the Passionist Community in Riverdale, New York.