Primer Very Weak

I found an easy fix! I measured the bore of the input fitting and found it to be 3/16". I went to the hardware store and purchased a 3/16" bearing ball. Due to tolerances, the ball is about 0.002" loose in the bore, which is perfect. The ball can move up into the body of the pump but cannot get stuck and returns to the bottom of the fitting by gravity creating an effective check valve. I bench tested the pump with the piping and injection nozzles using avgas and it works great. Looking forward to easier starts!

I have never seen a fitting modified like that, good luck in finding parts. I would look for a used primer out of a cessna or piper and install that.

Yes, Matt, this is a positive displacement pump and I would expect a check valve on each side. I suspect that parts have been lost some time in the past. I was hoping that this would be a common pump and I could find parts or a direct replacement.  This picture shows the pump body with the input and output fittings.  You can see the check valve in the output fitting.  The input fitting has no check valve and is a standard fitting.  The pump body has no internal valves except the shut-off pin on the end of the push rod, which only seats when the pump is in the "parked" position.
I will bench test the pump with the two orifices attached when I get the pump issue resolved.  I have looked for a check valve integral with the fitting shown but have been unsuccessful so far.

there is a check ball in both ports, it is usually a spring and a ball. You might want to pull the primer nozzles and clean them in Hoppes #9 gun cleaner.

I bought the airplane in May. It has never seemed right. I thought changing the o'rings might help. I agree, it seems like there should be a check valve on the input side. Hopefully someone may have experience with this model of primer.

I'm not familiar with this particular pump, but in any piston pump, if there isn't a check valve on the input side you are just pulling/pushing fluid in and out the input port. If there is no internal check valve (which isn't working), you may need another checkvalve fitting. Did this pump used to work but now it doesn't?