Backfires are not commonly fuel-related, though misfires are usually caused by a lean mixture or vacuum leak. Ignition related problems are more often the cause, I remember blowing 2 new mufflers to bits when a condenser wire in my distributor came loose (you can imagine how loud a backfire must be to detonate a muffler).
Anyway, it sounds like you are running an electronic ignition set up since you made no mention of ignition points or a condenser. One thing which can cause the problem you are describing is inadequate power to the electronic ignition system. The old points type ignitions would run with minimal power, but the newer electronic ignitions won't. If your alternator fails, or is not putting out much power, your engine will bog, and you'll get the same misfire problem you are describing.
If the problem is in fact fuel related, your carburetor may need to be re-jetted. The AFB uses 2 sets of jets, one for the primary side, and one for the second. The primary jets use step rods and springs which are vacuum controlled. The position of the step rod in the jet regulates how much fuel gets into your engine. The secondary jets are simple open jets like you would find in a Holley. Using metering rods with smaller tips will allow more fuel into the venturi when you step on the gas, you can access the step rods without taking apart the carburetor, they are held in place by two caps fixed by screws on either side of the carburetor, remove the screw, take off the cap, and remove the step rod with it's springs and piston. If you can't find a step rod with a small enough tip, you'll need to install larger main jets, but this involved getting further into the carburetor. You might start with the secondary jets first, you'll need to take apart your carburetor to get to them and find out what size they are, once you have them, pick up a couple more sets in progressively larger sizes, and see which works best. Adjusting the main jets on the primary side will also help, but it's hard to tell minor differences from the driver's seat. Back when I used to tune cars, dynos were rare, so tuning was done at the track, trying different jets, timing curves, etc. and using the clock at the track to see if these mods made the car any quicker.