'asseverate' originates from Latin, specifically the word 'asseverare', where the prefix 'ad-' (assimilated to 'as-') meant 'to' and 'severare' (from 'severus') meant 'serious' or 'stern'.

'asseverare' in Medieval/Latin usage meaning 'to make serious or to assert solemnly' passed into English as 'asseverate' (first recorded use in English in the 17th century) with little change in form but with a narrowed sense of 'to assert earnestly'.

Initially, it meant 'to make serious' or 'to treat seriously', but over time it evolved into its current meaning of 'to declare or affirm earnestly/positively'.