Sweetney went to Oxon Hill for high school, where he was named Washington Post All Met Basketball Player of the Year. He continued the tradition of highly skilled big men at Georgetown University, averaging 18.2 points while shooting nearly 55% over his three-year collegiate career. He was especially dominant over his junior year, in which he was named Honorable Mention All-America by AP, as well as being a Naismith College Player of the Year finalist and a candidate for the John R. Wooden Award.
That year, Sweetney was the only player in the nation to rank in the top 20 in scoring and rebounding. Despite playing only three seasons, he ranks seventh on Georgetown's career scoring list (1,750), fifth in rebounds (887) and sixth in blocks (180).
Sweetney was selected by the New York Knicks with the 9th overall pick, in the 2003 NBA Draft. After a two-year stint with only 42 regular season contests in his rookie year, he was traded to the Chicago Bulls on October 4, 2005, alongside Tim Thomas and Jermaine Jackson, for Eddy Curry and Antonio Davis.
Sweetney has battled weight issues throughout his life and career. It was reported in The Chicago Tribune that, if Sweetney did not lose a certain amount of weight, his career could be in danger. From 2007-09, he failed to make a single appearance.
In the summer of 2009 he played with the Boston Celtics summer league team. He was invited to attend training camp in October 2009 to try out with the Celtics and attempt to resume an NBA career. He was waived on October 22. In early December 2011, Sweetney rejoined the Boston Celtics for training camp, but he was cut on December 22, 2011.
On January 13, 2012, Sweetney agreed to a deal with the Vaqueros de Bayamon of the BSN, Puerto Rico's basketball league. In February 2013, he signed a one-month deal with the Venezuelan team Guaiqueríes de Margarita. After his contract expired, he returned to the Vaqueros de Bayamon. In February 2014, he signed with Club Atlético Atenas.
On May 1, 2014, he signed with Brujos de Guayama. He was waived on July 1, 2014.
In November 2015, after more than a year off, Sweetney signed a contract in Uruguay with Urunday Universitario.
Sweetney competes for Team City of Gods in The Basketball Tournament. He was a center on the 2015 team who made it to the semifinals, losing to Overseas Elite 84-71.