Latin 'arcus' meant both a bow and a curve — Romans saw the stone structure as analogous to a drawn bow.
A curved structure spanning an opening and supporting the weight above it; any curve resembling this.
From Middle English 'arche,' from Old French 'arche,' from Vulgar Latin *arca, from Latin 'arcus' (a bow, an arch, a curve). The PIE root is *h₂erkʷ- (to bend, to bow), which generated Latin 'arcuāre' (to bend like a bow), source of English 'arc'; the same root underlies 'arrow' through Germanic *arhjō (that which flies in a curve). The architectural arch, invented in the ancient Near East and perfected by Roman engineers, transferred
The prefix 'arch-' meaning 'chief' or 'principal' (as in archbishop, archenemy) has nothing to do with the architectural 'arch' — it comes from Greek 'arkhi-' (ruling, chief). Their identical spelling in English is pure coincidence, one of the language's more confusing homographic collisions.