An apparatus for delivering metered quantities of a fluid substance into a container, under the control of a programmable process unit, and a weighing device; a main storage tank is provided to fill by gravity a pressurizable auxiliary vessel connected to the inlet of delivery valves having different flow rates. The process unit is programmed to modulate the flow rates and to control the delivery time of the valves as a function of control signals received from a weighing device; the auxiliary vessel is hermetically sealed and connected to an air pressure source, to provide a constant pneumatic head in the vessel under the control of the process unit, at each delivery.