We can offer lots of guesses, BUT..............
Weber carburetor is like any other basic carburetor, venturis, float chamber and vents, float bowl, accelerator pump, fuel enrichment circuit.
The benefit of the Weber is that almost every circuit can be sized by jets, etc. to suit the application.
So if you do not know anything about carburetors, I recommend you get a Weber carburetor book, or two, or visit a few sites(Teglerizer, etc). That can fill you in.
Basic eyeball to see if the accel pump is working is engine off, air cleaner removed, open the throttle while looking down the throttle bore(with any choke plates held open) to see if you see a stream of gas being injected. Webers can size how big and how long that stream of gas is being injected. I would be more concerned that you do not have a fuel mounting problem(gasket leak or linkage interference with the manifold) and that the fuel pressure is proper, 1 1/2 to 3 maximum psi, and that the float level is proper.