Bigelow became the first ever female to take the top accolade at the glitzy Los Angeles event in March (10) for her gritty war drama The Hurt Locker, fighting off competition from her former husband's blockbuster Avatar.
But Weaver, who voices a character in Cameron's sci-fi epic, is convinced Bigelow only won the award because she's a woman.
She tells Brazilian news site Folha Online, "Jim didn't have breasts, and I think that was the reason. He should have taken home that Oscar."
The veteran actress is also disappointed that The Hurt Locker beat Avatar to the Best Picture prize - insisting the epic missed out on the trophy because it is "fashionable" for films that "nobody saw" to take the top prizes.
She adds, "In the past, Avatar would have won because they (Oscar voters) loved to hand out awards to big productions, like Ben-Hur. Today it's fashionable to give the Oscar to a small movie that nobody saw."