Seem to remember Weber’s have an extra little pump that squirts fuel into the inlet when the accelerator is pressed to stop this happening. Maybe blocked, faulty.
Sounds like a blockage in the pump jet. With the air cleaner removed check if, when you snap the throttle open manually there is a squirt of petrol from the pump jet. You could also check the integrity of the vacuum advance and retard hose as these can perish and cause a leak.
I had forgotten about the throttle pump. Yes I would agree that that could be a cause.
Though I think if that was the case it would still happen in cold weather.
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