Mike, I suggest you begin by downloading (free) the carburetor manufacturer's general service manual:
http://www.walbro.com/media/21936/SERVICEMANUAL.pdfNote that in general the WA model does not have an air purge pump, but yours does. It is not especially unusual for those pumps to stop working, though more often than not it is the bulb that fails, which is not the case with your carburetor. Here is the schematic of the carburetor, showing the detail of the air purge system pump, from the front cover of the manual:
You will see that for illustration purposes, a generic carburetor is shown: it happens to be a barrel-valve type which is quite different from yours internally. However we are only concerned with the air purge system pump, in the lower part of the carburetor. The purge system takes in fuel through the intake port on the right. This intake of fuel is sucked through the pumping and metering chambers, then is pushed out through the return hose on the left side of the pump, back to the fuel tank. It sounds as if one of the purge pump's check valves may be stuck open, but any other source of air leakage into the bulb would have the same effect. The manual refers particularly to the check valve below the fuel jets:
If you go to Page 25 of the manual (it will show as 27 on the Acrobat page counter), this is the beginning of the section on the air purge system. You can find there all of the nauseating detail on how it works and how to overhaul it. Please come back when you have read this, and we can go into detail.