A medical waste container comprises a bag with a flexible body defining a cavity and having a fill opening. A tube has a closed end in the bag and an opposite open end projecting from the bag. An elastic ring attached to the bag around the fill opening presses against the tube. A lip projects from the tube adjacent its closed end. A tab also projects from the tube, and a discharge opening is formed in the tube between the lip and the tab. A flow path extends from the open end of the tube into the cavity when the elastic ring encircles the tube at a first position between the tab and the open end. The ring slips over the tab from the first position to a second position in which the ring covers the discharge opening as liquid passes through the flow path, adding weight to the bag.