If it is running at the time it back fires your timing is off about 22 degrees. if it happnes when you are trying to start it then you timing is off 180 degrees.... Your intake valve is open when the spark plug fires.
Several things could make a carburetor backfire. The engine could be out of time. the carburetor could have a stuck float, or the engine could have a stuck valve.
Engine is out of time or the plug wires are installed incorrectly.
You may want to have the engine timing checked?
Loose intake boot or the boot may not be on straight. Happens everytime.
The timing may be off. If the timing belt is old then the gears can slip and cause backfiring, or the engine to not run at all.
it turns out the exhaust rocker was broken, replaced it and now it runs fine.
Water is in your engine. Check intake and head gaskets.
When water is put into a intake of a warm or hot engine, normally the engine will have valve damage, or possibley even crank shaft damage if a large amount of water (like from flood waters) was introduced.
It might be overfueled but it also might be just that when you turn the key off the motor runs on a bit and puts fuel into the hot exhaust and it ignites it and makes it backfire.
it would go slower and it might jerk
The engine turns the rotor through a transmission.
In three words: Bad ignition timing. Backfiring used to be very common in cars years ago, but electronically controlled "everything" in engine design makes it very rare today in an automobile.