Weber DCOE accelerator circuit leakage.

This shows leakage past the plugs for the accel circuit. This is only happening on one of the two carbs. The carb that IS leaking has different thread inserts than the good one. This is shown in the video.
Keeping in mind that anywhere fuel can leak, AIR can get sucked in as well. This very well may be the reason that this car is hesitating and has a slight surge at light throttle that will not clear up by simple rejetting or adjusting.
This problem can not be ignored in the diagnostic process, so it is time to replace the carb. It is also a good idea to replace both of them just so that everything is the same age and source.

[@pcallah3442]

Leaker looks like a third world country knock-off.

[@TheMike5232]

throw some teflon tape on it and call it good

[@GlennsMGRepair]

The video is instuctional for diagnosis. There are multiple ways to fix this, and certainly teflon tape or other methods can be tried if one wants to trust the rest of this carburetors quality.