'archedly' originates from English, specifically formed from the adjective 'arched' plus the adverbial suffix '-ly'.

'arched' developed in Middle English as the past-participle/adjective from the verb 'arch' (relating to a bow or curve), the root of which is traceable to Latin 'arcus' ('bow, arc') via Romance languages before becoming established in English; the adverbial form 'archedly' is derived by adding '-ly' to the adjective.

Initially it described a literal curved or bow-like shape ('in the form of a bow/arc'); over time it has also been used figuratively to describe a sly or knowing manner ('in a teasing or arch way').