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Sweeney agreed to a contract with the Bears on Sunday, Jordan Raanan of ESPN.com reports.
Sweeney began his career with Buffalo before linking up with the Giants last season. He suffered a "medical event" on the practice field in late August and never got into a game with New York, as he was eventually cut in late November. He'll now get a chance to compete for a roster spot among a tight end group that is led by veterans Cole Kmet (forearm) and Gerald Everett (knee).
