In 1992–93, Sweeney played in all 84 games and put up 36 points and ended up winning the Adams Trophy that year. In both the 1994–95 and 1995–96 seasons he was second amongst Boston defenceman with 22 and 28 points, respectively. In 1997–98, Sweeney missed the last 23 games of the season with a fractured shoulder that he suffered on March 1. In the next season, Sweeney achieved 205 hits and 85 blocked shots in 81 games. In the 1999–2000 season, he had 301 hits and 84 blocked shots, and in the following year he had 172 hits in 72 games and in 2000–01 season he contributed 18 points in 81 games. In the 2002–03 season, Sweeney scored only eight points in 67 games as his team nestled into third place in the division. On November 14 that year, he also played in his 1,000th NHL game.