Might be a big help to know WHAT carb we're fixing here...

..but good general advice by all ..
It could have clogged accelerator pump passages,or some carbs used a spring and steel check ball valve in the pump discharge jet,on many GM's they get pitted or dirty and the ball cant seal well and the pump loses its prime and wont squirt sufficient gas during acceleration..if it uses a accelerator pump diaphram it might be defective or leaky,or the stroke of the pump might be too short,the pump cup worn,etc..
Vacuum leaks at any hose like the PCV or power brakes,carb base gasket and intake can affect "take offs" more than idle or driveability sometimes..the secondaries on 4 barrels can stick open or open too soon and cause a bog,many times I have found vehicles with a bog or stumble on acceleration did not have any carb issues,it turned out to be vacuum leaks,bad vacuum advance unit on the distributor,late timing,bad plugs or wires that "snuff out" under a load,once I had an ignition coil with a crack let the spark leap to the small terminals (12V) to the high tention lead ,only when under acceleration..had defective ignition modules that crap out only under a load like take offs and had no dwell advance do it too..with points,bad bushings in the distributor shaft can cause a hesitation ..
I agree a hesitation on take offs IS a very annoying and one of the most dangerous things to have to put up with in city traffic..sometimes you cant afford to let it take its sweet time getting out there when entering an intersection or freeway..