Green’s Dictionary of Slang

(Scot./UK Und.) a fool.

1786		Burns ‘Twa Dogs’ in Poetical Works (1871) 6: For thae frank, rantan, ramblan billies, / Fient haet o’ them’s ill-hearted fellows.
1787		A. Shirrefs Jamie and Bess I i: How was the billy pleas’d; / Nae well, I wad, to be so snelly us’d.
c.1850		Duncombe New and Improved Flash Dict.
1865		Dundee People’s Jrnl 25 Nov. 2/5: Meantime the ither three billies had lunt it [lighted] their pipes also.
1901		G. Douglas House with Green Shutters 89: They claim to be bigger men and bigger fools than the Eastern billies.