1560s, "having equal alternate angles;" c. 1600, "sloping from the horizontal or vertical," possibly from Old French *baivel (Modern French béveau, biveau), which is perhaps from bayer "to gape, yawn," from Latin *batare "to yawn, gape," possibly imitative of yawning. But if so, the time gap is puzzling.
As a noun from 1610s, "tool or instrument for drawing angles and adjusting abutting surfaces;" 1670s as "an angle between adjacent sides." The verb, "to reduce to a sloping edge," is first recorded 1670s. Related: Bevelled; bevelling.