Green’s Dictionary of Slang

(Aus.) to swindle; thus balancer, a swindling bookmaker.

1895		Crowe Aus. Sl. Dict. 5: Balancer, one who pays part of his bets.
1900–10		Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 8: BALANCE: thieves and sporting to cheat in money or kind. Bookmakers who bet certain odds and if a winner only pay out the original stake or a portion of the winnings are called ‘balancers’. They are just a degree above welchers. To obtain anything on a false pretence or trick is also known as balancing.
1901		Sydney Sportsman (Surry Hills, NSW) 6 Mar. 3/3: ‘Welshing,’ ‘scaling’ and ‘balancing’ are unknown in Brisbane .
1906		Sun. Times (Perth) 23 Sept. 4/8: Then he balanced a bob from a silvery pal. / Who dropped four-and-six on the floor.
1907		Sun. Times (Perth) 4 Aug. 4/8: I’ve cut with takedown tugs / And buttoned for balancing books.
1941		Baker Popular Dict. Aus. Sl.
1955		N. Pulliam I Travelled a Lonely Land (1957) 230/1: balance – to cheat with money.