'asseverate' originates from Latin, specifically the word 'asseverāre', where the prefix 'ad-' (assimilated to 'as-') meant 'to/toward' and 'severus' meant 'serious'

'asseverate' came into English from Latin 'asseverāre' (Late Latin) via scholarly and legal Latin usage; the form and sense were carried into English from the 17th century.

Initially it meant 'to make a serious or solemn declaration' in Latin; over time it retained that sense and is used in modern English to mean 'to assert or affirm earnestly or solemnly'.