Fuel Problem - Carter BBS!?

Michael made some good points.

The amount of fuel in the bowl is controlled by the float acting on the needle. Make sure the needle and seat are in good shape and the internal passages are clean. Including the jet orifice and the bowl vent. Check and adjust the float. Relying on my memory, float specs on the BBS are usually 6-7 mm but you should condult a service manual.
It's a pretty simple carburetor, you should be able to fix this.