'arching' ultimately derives from the Old English root 'earc' (also seen as 'arc'), from Proto-Germanic sources related to the idea of a bow or arc.

'earc' in Old English developed into Middle English forms such as 'arch' or 'arc' and later gave rise to the modern English adjective and verb 'arch' and its present participle 'arching'.

Initially the root referred specifically to a 'bow' or 'arc' (a curved shape); over time it came to be used more broadly for things that form a curve and for figurative uses (e.g., a sly or playful 'arch' expression).