If the hesitation is only from idle, try setting the idle mixture control screws for a slightly leaner mixture.
If the hesitation occurs at any RPM when you try to accelerate, I would start eliminating possibilities (ie. timing, valves, distributor vacuum advance, fuel filter, etc.). After ascertaining that compression, valve timing, ignition, and fuel delivery system were all good, then it would be time to remove the top from the carburetor and check the condition of the vacuum pistons, vacuum piston springs, and metering rods.
Jon.
__________________
"Good carburetion is fuelish hot air". 
"The most expensive carburetor is the wrong one given to you by your neighbor".
If you truly believe that "one size fits all" try walking a mile in your spouse's shoes!
Owner of The Carburetor Shop, LLC (of Missouri).
Current caretaker of the remains of Stromberg Caburetor, and custodian of the existing Carter and Kingston carburetor drawings.
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