If carburated, it sounds like low speed or idling jet(s) is(are) dirty. Consider a carb cleaning and new plugs. Yes, check compression while the plugs are out.
you still have not posted the model #
what are the compression #s.
How did you clean carbs?
Did you do a link and sync after reinstalling carbs?
Have you checked timing ?
Do you have a manual to give procedures and specs?
May need to check voltages to the CDI and coils with a DVA or peak reading DMM