The couplet "Oh no, not my baby / Oh no, not my sweet baby" recurs throughout the song, and its being repeated so often evinces what the narrator himself says at the end of each verse: that he "kept on sayin'" this. Basically, the structure matches the meaning.
When I transcribed some of the lyrics, I also noticed an ambiguity in the line "She's not like these other girls you see." "You see" could function as a sort of interjection or as a headless relative clause describing the girls ("these other girls [whom] you see").
