The win capped a remarkable year for Clooney, who made Oscar history by becoming the first person nominated for acting in one movie and directing another.
Along with performing in "Syriana," Clooney directed the Edward R. Murrow tale "Good Night, and Good Luck," which earned him directing and writing nominations and was among the best-picture contenders.
In "Syriana," Clooney effaced his glamour-boy looks behind the bearded, heavyset facade of a CIA patriot who grows jaded over U.S. oil policy in the Middle East.
"All right, so I'm not winning director," Clooney joked, adding that an Oscar win always would be synonymous with his name from then on, including in his obituary. "Oscar winner George Clooney, sexiest man alive 1997, `Batman,' died today in a freak accident."
"This group of people gave Hattie McDaniel an Oscar in 1939 when blacks were still sitting in the back of theaters," Clooney said, referring to the supporting-actress winner from "Gone With the Wind," the first black performer to receive an Oscar.
In "The Constant Gardener," adapted from John le Carre's novel, Weisz played a humanitarian-aid worker whose fearless efforts against questionable pharmaceutical practices makes her a target for government and corporate interests in Africa.
Weisz thanked co-star Ralph Fiennes and director Fernando Meirelles, "and of course, John le Carre, who wrote this unflinching, angry story. And he really paid tribute to the people who are willing to risk their own lives to fight injustice. They're greater men and women than I."
The stop-motion family tale "Wallace & Gromit: The Curse of the Were-Rabbit" won the Oscar for best animated feature film.
Co-director Nick Park, who also made the hit stop-motion film "Chicken Run," thanked voice stars Helena Bonham Carter and Peter Sallis, who has done the voice of cheese-loving Brit Wallace for 23 years, since the filmmaker came up with the character in his student days.
"You've been an absolute gem, Peter, and you've sparkled all the way," Park said.
"King Kong," from "Lord of the Rings" creator Peter Jackson, won the visual-effects trophy. The Japan drama "Memoirs of a Geisha" earned the costume-design Oscar, while the fantasy epic "The Chronicles of Narnia: The Lion, the Witch and the Wardrobe" was picked for best makeup.
Clooney was one of the marquee names among a lineup of acting nominees heavy on lesser-known performers. And with a best-picture field of lower-budgeted films that drew smaller audiences than the commercial flicks that often dominate the Oscars, the question was whether Hollywood's big awards night could lure TV viewers.
Oscar organizers hoped new host Jon Stewart and the cultural buzz over front-runner "Brokeback Mountain" would beef up viewership.
Most of this year's nominees have turned a profit already, but there's not an 800-pound gorilla in the bunch, reports CBS News correspondent Jerry Bowen. That has some thinking that America won't care about a show that honors movies they haven't seen.
"Brokeback Mountain" is the most successful of the nominated films, taking in $75 million at the box office. But that ranks just 29th among all the films released last year. And "Capote," which has earned the least, ranks 104.
"Brokeback Mountain," though, has become a phenomenon far beyond those who have actually seen it, entering the pop-culture psyche with its tale of cowboys in love (best-actor nominee Heath Ledger and Jake Gyllenhaal, who had been among supporting-actor nominees).
The show began with reprise visits from former Oscar hosts Billy Crystal, Chris Rock, Whoopi Goldberg, Steve Martin and David Letterman, in which they all turn down offers to do the show again. Crystal and Rock did a "Brokeback Mountain" spoof, the two sharing a mountainside tent like the cowboys in the film and begging off as hosts, saying they were too busy.
Stewart used best-picture nominee "Capote," about gay author Truman Capote, to set up a "Brokeback Mountain" wisecrack, saying the film "showed America not all gay people are virile cowboys. Some are actually effete New York intellectuals. It's true."
Whether the "Brokeback Mountain" factor would boost ratings was uncertain. ABC, which airs the show, and the Academy of Motion Picture Arts and Sciences assembled an A-list collection of Oscar presenters to help offset a relatively unknown cast of nominees that included David Strathairn for "Good Night, and Good Luck," Terrence Howard for "Hustle & Flow" and Amy Adams for "Junebug."
Before the show, fans filled bleachers outside the Kodak Theatre, where principals of the documentary nominee "March of the Penguins" set a light tone, walking the red carpet with huge toy penguins.
"It's a little too warm here to bring real penguins," said director Luc Jacquet.
"I'm a nervous wreck," confessed Diana Ossana, a "Brokeback Mountain" co-nominee for adapted screenplay and also a producer on the film. "This is my first time at the Oscars, but I don't have any expectations."
"Brokeback Mountain" won top prizes at earlier Hollywood honors including the Golden Globes and was expected to earn best picture at the Oscars and the directing trophy for Ang Lee, who would be the first Asian filmmaker to receive that award.
Yet the ensemble drama "Crash," featuring a huge cast of characters in multiple story lines playing out over a chaotic 36-hour period, was a strong dark-horse contender to pull a best-picture upset.
Along with "Crash," "Brokeback Mountain" and "Capote," the other best-picture nominees were "Good Night, and Good Luck" and the assassination thriller "Munich."