'solidly-based' originates from the combination of 'solidly' and 'based', where 'solidly' means 'firmly' and 'based' refers to being founded or grounded.

'Solidly' and 'based' have been used in English since the Middle Ages, with 'solidly' deriving from the Latin 'solidus' meaning 'firm' and 'based' from the Old French 'baser', meaning 'to lay a foundation'.

Initially, it meant 'firmly grounded', and this meaning has largely remained the same in modern usage.