1570s, "a game played with a large inflated leather ball tossed, batted, or kicked back and forth," also the ball itself (1590s), from Italian pallone "large ball," from palla "ball," from a Germanic source akin to Langobardic palla (from Proto-Germanic *ball-, from PIE root *bhel- (2) "to blow, swell") + -one, suffix indicating great size.
The English word is perhaps also borrowed in part from French ballon (16c.), altered (after balle) from Italian pallone. Also see -oon.
The meaning "bag or hollow vessel filled with heated air or (later) hydrogen or helium so as to rise and float in the atmosphere" is 1784, after the Montgolfier brothers' flights. As a toy air- or gas-filled inflatable bag, from 1858; as "outline containing words in a comic engraving" it dates from 1844. Balloon-frame (n.) "structure of light timber fitted together to form the skeleton of a building" is from 1853.