Accelerator pump in carb isn't working.
With engine off, take air cleaner off the top of the carb, hold open choke plate and then pull open throttle, you should see gas squirting into throat of carb, alot of gas.
Accelerator pump is a diaphragm pump operated by an arm from throttle linkage, when you open throttle extra gas a squirted in to throat of carb for faster acceleration, hence it's name, accelerator pump.
If this isn't working then throttle response would be almost non-existent, and you would get what you describe, like back firing because air:fuel mix is too lean with throttle plate open and no extra fuel.
Main jets add fuel slowly as air flow increases past them, but can't react fast enough on quick changes in throttle position, so cruising along or slowly accelerating wouldn't be an issue, accelerator pump is only used when throttle is opened quickly, a pump action.
On some carbs you can install new diaphragm without rebuild, but it is often best to do the rebuild while carb is out since you have to get the rebuild kit to get new diaphragm.
It could also just be the arm has come off between accelerator pump and throttle linkage
Good read about 2150 carb here: http://grantorinosport.org/BubbaF250/carb/carb02.html