'grannyish' is formed from 'granny' + the suffix '-ish'. 'granny' originates as a familiar or diminutive form of 'grandmother' in English (ultimately influenced by Old French 'grand' meaning 'great/large'), and the suffix '-ish' comes from Old English '-isc' (from Proto-Germanic '*-iskaz') meaning 'of or pertaining to'.

'granny' developed as an informal/diminutive form of 'grandmother' in Middle English, while the adjectival suffix '-ish' has been used since Old English; the modern colloquial adjective 'grannyish' arose by combining them to mean 'like a granny'.

Initially 'granny' meant 'grandmother'; over time it also came to evoke associated traits (old-fashioned, matronly). Adding '-ish' shifted the word to an adjective meaning 'resembling or characteristic of a granny,' often implying old-fashionedness.