Lyric discussion by daborg 

Cover art for Enola Gay lyrics by Orchestral Manoeuvres in the Dark

'Little Boy' was the name of the bomb dropped on Hiroshima. 'Fat Man' was the bomb later dropped on Nagasaki.

Hence the references to being proud of little boy. Just to clear that up.

I think it also has the sense of the pilot's mother whou would be proud of the son. Like a double sided expression