More than 100 women have accused Weinstein of sexual harassment, sexual assault or rape over a 20-year period, since the publication of an article in the New York Times in October.
Weisz, 47, is a friend of British actress Sophie Dix, who has accused the producer of assaulting her in a hotel room when she was 22 years old.
“My friend Sophie Dix has been talking about this since the 1990s,” Weisz told the London newspaper.
“She would tell anyone who would listen her story, for the last 20 years. And no one seemed to care.
“I think his power was on the wane, the same with Bill O’Reilly, same with Charlie Rose (US news anchors).
“It’s about economics -— they weren’t turning over the big bucks any more,” she added.
However, she was optimistic that the scandal could still lead to real-world improvements.
“Let’s hope there’s some real structural change to come out of this. That women who don’t have huge platforms on Twitter, who are nurses or office workers, feel that they can talk to their bosses.”