An adapter assembly including a manifold and a valve assembly. The valve assembly includes a seat and a valve body having a circular base and a wall. The wall extends from a trailing side of the base to form a dome-like shape terminating at an end at which a slit is formed, with the wall defining opposing sealing edges at the slit. The seat has an upper circumferential surface and a lower circumferential surface. The upper surface engages a leading side of the base, whereas the lower surface engages a trailing side. At least one of the upper and lower surfaces forms a segment of increased height. Upon final assembly, the valve body is disposed across a passageway of the manifold, with the slit providing a selectively openable path. A force imparted by the segment of increased height flexes the base and biases the sealing edges into engagement.