'fat-based' originates from English, specifically the words 'fat' and 'base'/'-based', where 'fat' meant 'animal or plant fat' and 'base' (as in the verb 'to base') meant 'to found or place on a basis'.

'fat' comes from Old English 'fǣtt' (fætt) meaning 'fat, plumpness' (from Proto-Germanic roots), while 'base' comes from Old French 'base' and ultimately from Latin and Greek 'basis'. The compound 'X-based' (using the past-participle form 'based') developed in modern English to mean 'having X as a foundation or primary component'.

Initially the separate elements meant 'fat' and 'foundation'; over time the compound came to be used adjectivally to describe things that have fat as their primary base or constituent.