Sounds like it may be time for a carb rebuild. But before you do that you can try to adjust (tighten) the fuel mixture at idle:
First, check visually for any air tube blockage.
Otherwise, while engine is hot,
- screw the idle screw in several turns so the engine is idling fast, say 1500 - 2000 rpm
- tighten the fuel mixture screw until the engine stops running smoothly (begins to starve for gas), then turn back until its just smooth again.
- you can also play with the air-mixture at idle screw, turning it out to add air and effectively leaning out the mixture at idle (its easier to deal with one at a time though)
- adjust the idle screw until you're back at a normal idle speed.
This should make the carb as lean as possible without rejetting and should eliminate any fuel mixture complication that might be introduced by the idle speed circuit. If this fixes the problem at full throttle, you're done.
(On the down side, if you set the mixture at idle too lean, the engine may tend to overrun on shutdown, if this happens, unscrew the mixture screw 1/8 turn and try again).
If this doesn't work, look to the full-throttle circuit for the problem (fuel bowl, float, main jet, atomizer, and tapered needle). The most likely problem, is debris blockage or varnish built up on the jets and needles and one or more that may have to be cleaned and reseated. Second most likely is physical damage (bent needle). You may need a carb kit to fix these types of problems