Stone and Weisz are joined in the supporting actress category by Nina Arianda for Stan & Ollie, Rachel McAdams for Disobedience and Molly Wright for Apostasy.
Both actors are also nominated in the supporting actress category.
Winners will be announced at the British Independent Film Awards ceremony on December 2 at London’s Old Billingsgate.
All three are nominated for best British independent film, as is Disobedience.