He spent his career in curatorial and leadership positions at the Winterthur Museum, Garden and Library.
Henry Francis du Pont mentored Sweeney and, after Jacqueline Kennedy appointed du Pont to chair the Fine Arts Advisory Committee tasked with renovating the White House's decorations and furnishings, appointed Sweeney to serve on the committee in 1961.
Sweeney played an influential role in turning du Pont's personal collection of American decorative arts into one of the leading decorative arts museums in the United States.
He also recommended the establishment of the Joseph Downs Manuscript Collection to honor Winterthur's founding curator, who died in 1954.
[5] He served on the boards of the Decorative Arts Trust, the Victorian Society in America, the University of Delaware Library, and Rockwood Museum and Park.