Originally darts were made of wood and imported in their hundreds of thousands from France. (Yes, darts is (partly) French!!!) To begin with they were only available in one weight but then lead was added either around the barrel (a process called 'banding') or 'injected' into the barrel (called 'loaded') and thus variations of weight (usually light, medium and heavy) appeared.
As far as I can tell, brass was always the metal of choice for darts manufacture until of course tungsten arrived. It was easily machineable but also resilient and strong. I have a catalogue dated 1929/30 which shows the wooden French darts as well as brass "Trueflight" darts (manufactured by NODOR) and 'cane and brass ferruled darts', the latter 'Light' retailing at nine shillings (that's 45p) for a box of three dozen darts!