'archwise' originates from English, formed by combining the adjective 'arch' and the suffix '-wise' (from Old English 'wīse' meaning 'manner' or 'way'). The element 'arch' in the sense 'curved' ultimately traces to Latin 'arcus' ('bow, arch').

'archwise' developed in English as a compound of 'arch' + '-wise' (Middle/Early Modern English formation pattern). The literal sense was 'in the manner of an arch'; by later usage the adjective 'arch' (meaning 'playfully roguish') influenced a figurative sense 'in an arch manner.'

Initially it meant 'in the manner of an arch' (literally curved), but over time it also gained the figurative sense 'in a playfully roguish or mockingly playful manner.'