The story
Derived from slang fatty (“a fat person”) + bom bom ("a sound imitative of the noise a fat person makes when walking"). Compare West Indian/Caribbean slang fatty bum-bum ‘a very fat person, esp. a woman with large buttocks’ (Dictionary of Caribbean English Usage (1996), Green’s Dictionary of Slang), and Australian slang fatty boom-bah or fatty-boom-bah-sticks ‘a taunting nickname for a fat person’ (The Essential Lingo Dictionary of Australian Words and Phrases, 2015).
Etymology from Wiktionary, CC BY-SA 4.0.