Yes, the Columbia was the heaviest of the Shuttles, but it was planned to fly to the ISS later this year carrying the first teacher in space. Columbia was capable of flying to the ISS but not with much in the way of payload. Here's an article from January with the following info:

Shuttle Mission STS-118 (Columbia)
Launch: No earlier than Nov. 13, 2003
Objectives: ISS 13A.1 -- Deliver Starboard-side truss segment 5 (S5); Educator Astronaut flight
Spacewalks: Three
Crew: Commander Scott Kelly, Pilot Charlie Hobaugh, Mission Specialists Scott Parazynski, David Williams and Lisa Nowak, and Educator Astronaut Barbara Morgan