After three decades as a stand-up comedian, Sweeney was a relative latecomer to the acting profession. He made his television debut alongside Kenneth Branagh, in 1982's Too Late to Talk to Billy. A number of minor roles in acclaimed films such as The Crying Game (1992) and The Butcher Boy (1997) followed. However, it is as irascible farmer Eamonn Byrne, in long-running BBC series Ballykissangel, that Sweeney is most fondly remembered.

Story centres around seventy-year-old Tommy who must choose between two women when an old flame turns up in his life.