I'm new to the world of automotive cars. But I have a LOT of motorcycle carb experience.
Idling properly but not being able to accelerate under heavy throttle (bog, popping) generally means your mains got dirty / clogged from old gas.
I could be out of line here since I haven't torn into Webers yet - but if they are like any mikuni / keihin, your mains are clogged.