In the first award of the night, Clooney appeared surprised as his name was announced for his role in the political thriller "Syriana."
First saying he thought Paul Giamatti was going to win for "Cinderella Man," Clooney then apologized for his nerves: "This is early. I haven't had a drink yet."
Britain's Weisz was much more subdued as she regally thanked everyone involved her film, "The Constant Gardener."
Hollywood veteran Paul Newman took the Golden Globe for supporting actor in a series, miniseries or TV movie for his role in HBO's miniseries "Empire Falls." He did not attend the ceremony.
Sandra Oh won the best supporting TV actress for her role as a doctor on ABC's "Grey's Anatomy."
"I feel like somebody set me on fire," she said.