'unfussily' originates from English, specifically from the adjective 'unfussy' formed with the prefix 'un-' and the word 'fussy', where 'un-' meant 'not' and 'fussy' came from the noun 'fuss' meaning 'a display of unnecessary excitement or attention'.

'unfussily' developed by adding the adverbial suffix '-ly' to 'unfussy' in Modern English; 'fuss' entered English in the 18th century (possibly from dialectal 'fus' or as an imitative formation) and 'fussy' derived from that noun.

Initially the parts meant 'not' + 'showing fuss'; over time the formation with '-ly' retained this basic sense, giving the adverb the current meaning 'in a not-fussy manner' or 'without unnecessary show'.