Dench is up for the Best Actress Award at the British Academy of Film and Television Arts (BAFTA) ceremony on Sunday (16Feb14) and she is also nominated for an Oscar for her performance in Philomena.
However, she has not been able to take part in the usual promotional campaign ahead of the ceremonies as she is still recovering from a knee replacement operation.
Weinstein, whose self-titled film company is behind Philomena, fears not being on the campaign trail will put Dench, 79, at a disadvantage to her younger competitors such as Cate Blanchett and Amy Adams.
He tells Britain's Daily Telegraph newspaper, "Honestly, it's been tough for her, health-wise, and she hasn't done the kind of campaigning the others have. She hasn't been able to do the interviews... I'm not talking out of school - I'm sure she'll recover magnificently - but she's had a tough time of it this year, physically.
"Cate Blanchett has had the luxury of being in a lot of places... Amy Adams has been very visible at awards shows and everything else."
Dench will compete against both Adams (American Hustle) and Blanchett (Blue Jasmine) at the Bafta ceremony, along with Emma Thompson (Saving Mr. Banks) and Sandra Bullock (Gravity).