Fat Man and Little Boy is a 1989 film that reenacts the Manhattan Project, the secret Allied endeavor to develop the first nuclear weapons during World War II. The film is named after the weapons “Little Boy” and “Fat Man” that were detonated over Hiroshima and Nagasaki, respectively. The film was directed by Roland Joffé and written by Joffe and Bruce Robinson.
https://en.m.wikipedia.org/wiki/Fat_Man_and_Little_Boy
Ahhh... does strike a bell. As to the flick - popular culture is somewhat lost on me; besides, in 1989 I was recovering from being hit by lightning... (Don't stand too close! 😵)