(written from a Production point of view)
Weber is best known for his role as Brian Michael Hackett on the hit television sitcom Wings. Prior to this, Weber had a one-year stint on the soap opera As the World Turns, from 1985 through 1986.
In 1990, Weber played John F. Kennedy in the mini-series The Kennedys of Massachusetts, co-starring fellow Deep Space Nine guest actor Tim Halligan. The following year, he appeared on Tales from the Crypt along with Frank Kopyc and Vincent Schiavelli.
In 1997, Weber starred in the mini-series remake of the Stephen King horror movie The Shining. His portrayal of Jack Torrence earned him a Saturn Award from the Academy of Science Fiction, Fantasy & Horror Films. In 2006, he appeared in another mini-series based on a Stephen King story, Desperation, co-starring Ron Perlman and Matt Frewer.
Weber also appeared in multiple episodes (especially in the last season, when he was a regular performer) of Once and Again, starring with William O. Campbell, Jeffrey Nordling and Susanna Thompson. One episode in which he appeared also guest-starred David Clennon; and he appeared with Saul Rubinek in both of the latter's appearances on that series. In 2003, he co-starred as a psychotic murderer opposite Star Trek: Voyager stars Roxann Dawson and Robert Picardo, as well as Scott MacDonald, Dakin Matthews, and Rick Worthy, in an episode of the short-lived law series The Lyon's Den entitled "Trick or Treat". He also starred in the series The D.A., which lasted only four episodes in 2004, and appeared in two episodes of Will & Grace as Sam Truman. Weber played the regular role of Jack Rudolph in Studio 60 on the Sunset Strip (2006-2007, with Cyia Batten), and had a guest appearance on Desperate Housewives as the much older boyfriend of Teri Hatcher's daughter. In 2015, he portrayed Brother Michael in the SyFy series Helix opposite William O. Campbell.
He has also lent his voice to several animated series, including The Simpsons, All Dogs Go to Heaven: The Series, Baby Blues, and Seth MacFarlane's American Dad!, the latter of which also featured the voice of Patrick Stewart. In Disney's Hercules series, Weber voiced Odysseus.
Weber has also appeared in numerous feature films, beginning with 1984's The Flamingo Kid, which also features fellow Star Trek alumni Googy Gress and Brian McNamara. His later film credits include Hamburger Hill (1987), Single White Female (1992, also featuring Kenneth Tobey), The Temp (1993, co-starring Dwight Schultz and Dakin Matthews), the acclaimed Leaving Las Vegas (1995, with Thomas Kopache and Ed Lauter), and Mel Brooks' Dracula: Dead and Loving It (1995, co-starring Clive Revill). He also co-starred with Star Trek: The Next Generation's Patrick Stewart and Voyager's Ethan Phillips in the American gay comedy Jeffrey.
More recent film credits include 1998's I Woke Up Early the Day I Died (co-starring Lee Arenberg, Ron Perlman, Mark Rolston, and Carel Struycken), 2000's Timecode (with Golden Brooks), and 2006's The Moguls.
From 2014 through 2017, Weber held a recurring role on NCIS: New Orleans as New Orleans mayor (and nemesis to Dwayne Pride), Douglas Hamilton. Pride was played by Scott Bakula.