Well I don't know about Weber carbs but usually the carb is useing the idle circuit(engine is idling) when you shut the engine off. To backfire on shutdown means it is running lean in the idle circuit or actual timing is way off. If the weber has idle screws, have you messed with them? With my non-comp. BBD I went buy tune-up specs but also used a vacuum gauge for highest pull, evenly adjusting both screws. Good Luck.

Huh?