c. 1300, ballede, "wanting hair in some part where it naturally grows," of uncertain origin. Perhaps with Middle English -ede adjectival suffix, from Celtic bal "white patch, blaze" especially on the head of a horse or other animal (from PIE root *bhel- (1) "to shine, flash, gleam"). But Middle English Dictionary says probably formed on the root of ball (n.1) and compares Old Danish bældet.
Compare, from the same root, Sanskrit bhalam "brightness, forehead," Greek phalos "white," Latin fulcia "coot" (so called for the white patch on its head), Albanian bale "forehead." But connection with ball (n.1), on notion of "smooth, round" also has been suggested, and if not formed from it it was early associated with it. Sometimes figurative: "meager" (14c.), "without ornament" (16c.), "open, undisguised" (19c.). Of automobile tires with worn treads, by 1930. Bald eagle first attested 1680s; so called for its white head.