You have mentioned the problem already. My suggestion is to remove the Weber 34ICH and use it as a doorstop. They're
****. Originally designed for an 1100cc Ford engine. It has it's supporters but I'm not one of them. Use a correct spec Zenith 36IV (or indeed a later "Solex" 36IV labelled unit, which is identical) or better still find a pre-1967 Solex PA40 carb, if you can, and you will find it more torquey, less thirsty, and all together a smoother drive.