I would say, give the carb a good cleaning with parts cleaner. Then see how it runs...
If it only happens on low vacuum (below 10" Hg or less), then it may be in the power enrichment system (power valve/metering rods)..
Put a vacuum gauge on it and see what vacuum it hesitates at and what vacuum it goes away or if it stays at all vacuum levels...
Hook the vacuum gauge to intake vacuum off the intake or at the base of the carb...
If it happens at high and low vacuum, then you may have some build up in the jets and main system... Then the carb needs to be cleaned out/rebuilt.. [this may be your case as it fits what your describing].. .