The 2004 picture was released by Moore's Westside Productions via a deal with the Weinsteins' The Fellowship Adventure Group. It became the highest-grossing documentary of all time with worldwide profits of $222 million (£148 million).
But Moore claims the Weinsteins reneged on their agreement to share the profits equally between the two firms and has accused the moguls of secretly syphoning off cash for their own benefit, according to TMZ.com.
Legal documents filed by Moore's lawyer, Larry Stein, alleges the Weinsteins used "bogus accounting methods to hide the true amounts due (to) Westside".
Moore is seeking more than $2.7 million (£1.8 million) in compensation.