do you have the original fuel filter with the return line? the return line should be on top so the filter wont drain.
weber carbs are known for being hard starting after sitting a while but not so bad that they have to be primed.
if your fuel pump is working like you say it should fill the bowl after cranking a bit and it should start without priming.
I know you say you checked the pump but maybe its weak, heres a link to the proper way to test
How to Test Mechanical Fuel Pump | eHow