1590s, "to assign quarters to, to direct (a soldier) by note to a lodging place," from a noun meaning "a ticket given by a military officer directing a person to whom it is addressed to provide board and lodging for the soldier carrying it" (1640s). This was a specific use of the word, which earlier meant merely "official record or register" (late 13c.), from Anglo-French billette "list, schedule," diminutive of bille "written statement" (see bill (n.1)) with -let. From 1830 in the sense "place where a soldier is lodged." Related: Billeted; billeting.
"short, thick stick of wood used for fuel," mid-15c., from Middle French billette, diminutive of bille "stick of wood," from Medieval Latin billia "tree, trunk," which is possibly from Gaulish (compare Irish bile "tree trunk").
"small paper, short document, note," mid-15c., earlier "an official register, roll, or record" (late 13c.), from Anglo-French billette "list, schedule," diminutive of bille "written statement" (see bill (n.1)) with -let.