Before election to the episcopacy, Weaver served the Western Pennsylvania Conference as a pastor. He entered the ministry in 1967 as a deacon and was ordained an elder in 1969. He held appointments as:
Pastor, Whitaker United Methodist Church, 1971-77
Senior Pastor, Smithfield United Church (UCC and UMC), Pittsburgh, PA, 1977-88
Senior Pastor, First United Methodist Church, Pittsburgh, PA, 1988-96
He was elected a bishop of the United Methodist Church by the North East Jurisdictional Conference in 1996. He was then appointed to the Philadelphia Episcopal Area where he presided over the Eastern Pennsylvania Conference and the Peninsula-Delaware Conference until 2004. Weaver was then assigned the Boston Episcopal Area where he continues to serve the New England Conference.
Weaver served his colleagues as President of the UMC Council of Bishops (2003-04). He was the first president bishop since the council increased the office's term to two years. The council comprises 50 active bishops in the United States; 18 bishops in Europe, Asia and Africa; plus 96 retired bishops worldwide. They are the top clergy leaders in the nearly 11 million-member church.