The Carter WA-1, 1 barrel carburetor can have one check ball in some cases and in other cases, 2 check balls. Most WA-1 will need both check balls.
Both types will need a check ball in the main discharge tube. When you have two check balls in the carburetor kit, install the bigger of the two in the main discharge. When required and for most WA-1 carburetors place the smaller (and sometimes aluminum) in the accelerator pump well.
To determine if you need a check ball in the accelerator pump well, look at the bottom of the well. When a check ball is required, you will have two holes at the bottom. One on the bottom and another slightly up the side. The bottom hole is the intake and is where the check ball is installed. The hole on the side is where the fuel is discharged when you press on the gas.
Your WA-1 can have a couple different types of main discharge nomenclatures. The most popular will have the check ball placed in the discharge tube 1st, then the plug (small stem on the plug) is installed. The 2nd type had a check ball, then a small spring that sits on top of the check ball, then the plug (no small stem).
The check ball in the bottom of the accelerator pump well is used to plug the hole when the pump is pumping fuel out to the discharge, otherwise the fuel will go back into the float bowl instead. If you have hesitation on acceleration, check to make sure your check ball isn’t missing.
The check ball in the discharge tube is used to close off the discharge when fuel is entering the pump well on the up stroke (off accelerator). When this is going on, you don’t want fuel being sucked into the venturi by vacuum. The check ball is there to keep that from happening.
Watch a video about this.