He also appeared in several Shakespeare plays on Broadway, and in the original production of Eugene O'Neill's The Iceman Cometh, as Harry Slade.
Sweeney made minor appearances in several major films, including The Crying Game (1992), The Snapper (1993) The Butcher Boy (1997), and Angela's Ashes, and made his stage debut in the 1989 Dublin production of The Iceman Cometh at the Abbey Theatre.