As you can tell it can be a wide variety of things, so start by trying to rule things out.
1. It's not the needle adjustments. It would either run poorly pretty consistently at one throttle setting, cough and sputter when you advanced the throttle, or stop dead. Ditto for the fuel system.
2. It may be that the receiver is going into failsafe, and it is incorrectly set. Pretty unlikely if you still had control of all the other functions, but read up on it for your system and double check how to set it. Typically it should go to idle when failsafe happens, but yours may be set backwards. You could stake it to the ground while running at part throttle, and see what happens when you turn the TX off.
3. If the batteries are clipped into a battery holder, they may be momentarily losing contact. Best would be to swap for a pack that is all one piece (batteries actually welded together). But check all the connections to make sure they are strong. Wrap the pack (any kind) in lots of foam rubber. Install so that it is in firm, but not strapped tight - the foam needs give to be able to reduce engine vibrations. Ditto on the receiver. Use real hobby store foam rubber. At least 1/4" thick all around. 1/2" is even better. If it is a battery problem, you would be losing all the other controls too. But test to eliminate it as a possibility.
4. Try a new switch, or for a couple of test flights, skip the switch and plug the battery directly into the receiver. May not be practical if it is a pain to get at them. Ditto on all the other controls going out if it is a switch problem, but if you can test it would eliminate one more possibility.
5. While your system is "affordable", it's not a bad system, so again unlikely to be the problem, unless everything else is tried.
6. Do a range check - how to should be in the radio instructions. Do it with both engine off, and then when running. Distance where you begin to loose control should be about the same.
7. Look closely at where the throttle plugs into the receiver - is it tight, undamaged, with no damaged wires?
8. Make sure the servo is not somehow partially coming loose.
9. As the Wasp noted, make sure the pushrod connections at both ends are solid.
10. Unlikely to be the carb, but do as the Wasp said, and make sure it is seated well. Go over all the engine bolts checking for looseness (but don't crank them down super duper tight!)
11. Make sure the engine is mounted solidly - no wiggle at all.

If after all the above seems to pass, I'd blame the servo...throttle doesn't need anything high end, cheap is fine. Going through the above first also gives you a check on the rest of the system, to verify you aren't seeing any quirks there.