Green’s Dictionary of Slang

(UK Und.) a thief who specializes in stealing tradesmen’s shop books.

1734		C. Johnson Hist. of Highwaymen &c. 193: She became acquainted with a new Sort of Thieves, call Heavers, whose employment was stealing Shop-Books from Drapers and Mercers.
c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Heavers. Thieves who make it their business to steal tradesmen’s shop-books.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn).
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1897		C. Whibley ‘Moll Cutpurse’ in Book of Scoundrels 59: She is remembered [...] not only as the Queen Regent of Misrule, the benevolent tyrant of cly-filers and heavers, of hacks and blades, but as the incomparable Roaring Girl.