A system is provided for weighing and monitoring flow from multiple fluid sources into a flow system wherein incoming fluid is received in a weighing bag attached to a control system for monitoring the amount of fluid passed through the weighing bag and for preventing admission of air into the flow system. An alarm attached to the weighing bag warns when fluid in the weighing bag is approaching empty, so that the fluid in the weighing bag can be replenished from the fluid source before the weighing bag runs dry. If fluid in the weighing bag is not replenished, the system automatically shuts down.The fluid pump can be absolutely calibrated using the controlled admission of known amounts of fluid into the weighing bag so that the amount of fluid introduced into the flow system through the weighing bag can be calculated automatically.