Warner Bros responded with a statement calling the Weinsteins' sale of Tolkien's book rights "one of the great blunders in movie history".
The studio said the Weinsteins and Miramax agreed to be paid only for the first film based on each book.
"No amount of trying to rewrite history can change that fact," Warner Bros said. "They agreed to be paid only for the first motion picture based on The Hobbit. And that's all they're owed."
The rights to Tolkien's books were owned by Miramax, which was founded by the Weinsteins. After trying to develop the movies, they sold the rights to New Line (which later merged with Warner Bros and is owned by Time Warner) in 1998 for 5 per cent of the profits on each film.
The Lord of the Rings films grossed nearly US$3 billion worldwide. With The Hobbit: An Unexpected Journey, the movies have each netted the Weinsteins more than US$100 million. Although the Weinsteins have since sold Miramax to Disney, they retained a share in The Hobbit profits.
The dispute will hinge on how the 1998 agreement is interpreted. It reads that the terms apply to "the first motion picture, if any, based in whole or in part upon such book which is produced ... but excluding remakes".
The Weinsteins' suit alleges that the three Hobbit films are installations of one movie, noting that director Peter Jackson largely shot all three at once.
"We are surprised and frustrated by the position Warner Bros is taking with regard to The Hobbit franchise," Bob and Harvey Weinstein said in a statement.
"Since the beginning, Miramax, Harvey and Bob have been a force in getting these books to the screen. In fact, they funded the initial technology for the films at Peter Jackson's (special effects company) Weta. Without these early investments, none of these pictures would have been made."
The third Hobbit film, There and Back Again, is due out next December.
- AP