Does the engine also have trouble shutting off right away? If yes, then the hesitation could also be caused by an air leak around the carb body where it enters the engine. To fix this, pull out the black hex screw hoding the carb in place and smear a small amount of automotive silicone sealant around the body of the carb and on the screw then reassemble. it does wonders. Use ULTRA GREY,BLUE or COPPER. I had the same problem you describe and it was both in need of a low end needle adjustment and air leak sealing. Now it runs better then when new.