'legitimately' originates from Latin, specifically the word 'legitimus,' where 'leg-' meant 'law.' 'Gained' comes from Old French 'gaigner,' meaning 'to earn or win.'

'Legitimus' transformed into the Medieval English word 'legitime,' and eventually became the modern English word 'legitimate.' 'Gaigner' evolved into the Middle English 'gainen,' leading to the modern 'gain.'

Initially, 'legitimus' meant 'lawful,' and 'gaigner' meant 'to earn.' These meanings have largely remained the same in modern usage.