Her space shuttle flights include the Discovery mission in July 1995 to launch NASA's TDRS-G communications satellite, and the Atlantis mission in May 2000 to construct the International Space Station. She logged more than 450 hours in space. Weber was selected as an astronaut in 1992. She was the Legislative Affairs liaison with Congress at NASA Headquarters in Washington, DC, in 1995, and resigned from NASA in 2002. She went on to be the associate vice-president at the University of Texas Southwestern Medical Center in Dallas.