Contrary to popular belief, one of the most common causes of hesitation from a dead stop is the idle being set too rich. This often occurs when the idle is set with a vacuum gauge. The overrich mixture combined with little air velocity causes "puddling" in the intake. When the throttle valve is opened, the additional air sweeps the puddles into the cylinders causing an instantaneous overrich condition, and a hesitation.
Another common cause of hesitation is faulty ignition.
And, of course, the accelerator pump certainly can cause a hesitation. However, when I was a kid in the 1940's and 1950's, it was common practice among farmers in rural Missouri to disconnect the accelerator pump completely in an effort to save fuel.
Check the other "possibles" first.
Jon.
