'balsamically' originates from Modern English, formed from the adjective 'balsamic' plus the adverbial suffix '-ally'; 'balsamic' itself comes from New Latin 'balsamīcus', ultimately from Latin 'balsamum'.

'balsamum' in Latin was borrowed from Greek 'balsamon', which in turn came from Semitic sources (e.g. Hebrew 'basam'/'bosem' or Arabic 'balsam'), and the form evolved through New Latin into English 'balsamic' and then 'balsamically'.

Initially it referred specifically to 'of or relating to balsam' (the aromatic resin); over time it broadened to mean 'having soothing, restorative, or pleasantly aromatic qualities', and as 'balsamically' it means 'in a soothing or balm-like manner'.