How The Accelerator Pump Works
Hesitation can be caused by electrical (usually distributor), as well as by the carburetor accelerator pump circuit.
In order of probability:
--- Discharge needle is not properly seated; tap with a punch and hammer, then test by holding down needle with punch while accel. pump is manually depressed.
--- Pump plunger is defective. If pump plunger goes down but no fuel escapes past needle in above test, plunger is bad. (We see this with new pumps more often than you might think!)
--- Pump springs installed in wrong position. Weak spring must be on bottom, strong spring on top of pump beneath keeper.
--- Left hand float level is set too low, hence fuel level is insufficient. If fuel does not stand above bottom of slot in side of pump cylinder, pump won't draw fuel into the cylinder on the intake stroke.
I'll bet that the problem is one of those above, if not some combination of thereof.
Tip - The AFB pump link, links the pump lever to the accelerator pump. When you look at the link installed from the front of the carburetor, it should look like a 'S'.