On TV, Weber guested on "Crime Story" (NBC, 1987) and appeared in the movies "When We Were Young" (NBC, 1989) and "Fatal Flaw" (ABC, 1989). He gained notice as the young John Kennedy in the mini-series "The Kennedys of Massachusetts (ABC, 1990), before his real break came that same year. He was cast as Brian Hackett, the irresponsible charmer on NBC's hit sitcom "Wings" (1990-97), and soon other offers began coming in as well. He co-starred in a handful of TV movies, including "Deceptions: A Mother's Secret" (NBC, 1991), "In the Company of Darkness" (CBS, 1993), and "Betrayed by Love" (ABC, 1994).
Buoyed by "Wings", Weber returned to the big screen in Barbet Schroeder's "Single White Female" (1992), as Bridget Fonda's loutish, ill-fated boyfriend. After a supporting role in "The Temp" (1993), he starred for the first time in "Jeffrey" (1995), based on Paul Rudnick's play about a gay man trying to be celibate. He followed this with a cameo in the acclaimed drama "Leaving Las Vegas" and in Mel Brooks' "Dracula: Dead and Loving It" (both 1995). In the latter, he played straight to Leslie Neilsen and was teamed romantically with his "Wings" co-star Amy Yasbeck. Divorced from Carter, Weber wed MTV executive Juliette Hohnen in 1995.