Abstract: A pumping system with inlet and outlet check valves for delivering measured doses of liquid from a reservoir container, which might include sterile normal saline solution, to a series of smaller vials or hypodermic syringes. This pumping system has an improved valve system that includes a heavily biased check valve and a lightly biased check valve. An embodiment of the system has a valve body with an inlet passage surrounded by a valve seat, and an outlet valve member is biased against this valve seat by a pressure that is substantially greater than a pressure biasing an inlet check valve against its valve seat. A heavy bias at only one valve both (1) prevents valve leakage from the system due to a liquid pressure head from the reservoir container and (2) reduces operator fatigue.