Weisz earned the best actress title from the critics for her performance in The Deep Blue Sea, a period drama by the British director Terence Davies.
Day-Lewis won one of three awards for Steven Spielberg's Lincoln, when he was named best actor for his portrayal of the former US president - giving him his fifth gong from the NYFCC. Co-star Sally Field was named best supporting actress and Tony Kushner won the award for best screenplay.
"Zero Dark Thirty confirms the massive talent of Kathryn Bigelow," said NYFCC chairman Joshua Rothkopf, a critic for Time Out New York. "Zero Dark Thirty is a very important movie. It's not triumphant and it's still a very significant dramatisation of an important event. And we were knocked out by the film."
The supporting actor pick went to Matthew McConaughey for his performances as both a Texas district attorney in Richard Linklater's Bernie and as a male stripper in Steven Soderberg's Magic Mike. Shut out entirely were awards hopefuls Les Miserables, Argo, Silver Linings Playbook and The Master.
Michael Haneke's Palme d'Or-winning Amour took best foreign language film. Best non-fiction film went to The Central Park Five, the documentary about the infamous 1989 New York rape case.
Best animated film went to Tim Burton's Frankenweenie. The Aids activism documentary How To Survive A Plague was picked as best first feature.
The New York Film Critics Circle, a body of 35 New York-based critics founded in 1935, announced their annual vote on Twitter over a period of hours. Awards will be handed out at a ceremony on January 7.