"of or pertaining to the islands in the Mediterranean just east of Spain," 1660s, from Latin Balearicus, from Greek Baliarikos, from the ancient name of the islands and their inhabitants; traditionally "the slingers" (from ballein "to throw, sling") in reference to their weapons.
in 19c. American English political jargon synonymous with "Democratic Party in New York City," hence, late 19c., proverbial for "political and municipal corruption," from Tammany Hall, on 14th Street, headquarters of a social club incorporated 1789, named for Delaware Indian chief Tamanen, who sold land to William Penn in 1683 and '97. Around the time of the American Revolution he was popularly canonized as St. Tammany and taken as the "patron saint" of Pennsylvania and neighboring colonies, sometimes of the whole of America. He was assigned a feast day (May 1 Old Style, May 12 New Style) which was celebrated with festivities that raised money for charity, hence the easy transfer of the name to what was, at first, a benevolent association. The club's symbol was a tiger.