I might have had this same problem because we got my choke set just right on my car. Then one day we tried to start it and it was acting like it was not choking. Turns out we must have not tightened it. My grandpa did this so I realy don't know how you tighten it. Hopefully It doesn't come lose on me again.

Alo I am guessing you have an elecctric choke? That is what I have.

 

Which end is loosening? Pic?

 

As I actuate the choke this screw that holds the lever in place comes undone on its own and I don't know how to fix it.

 

I will expand on what he said...'Blue'.

Need to determine if it is vibrating loose or if the lever is dragging. If the lever is dragging, should it be rotating freely? If there is some sort of bind, locate on the screw might bind it up. Something could be missing to give some clearance?

 

The bolt that holds the rotating lever goes thru a stepped bushing (my Weber book calls them "bushing for loose lever") that allows the lever to rotate independently of the bolt, and allows the bolt to be tightened down without binding the lever. Is that perhaps missing? I would have to disassemble a spare Weber to show you what the bushing looks like. Here is a photo of the Weber DGV, and the bushing is #74

 

I have all the pieces for the loose lever mechanism but it still drags the screw one way to loosen it so I don't know whats going on.

 

to add on the screw only stop loosening when its so loose that the loose lever is able to move up and down which I do not believe should be happening. when I hold the screw in place with a screwdriver and move the lever (off the carb) it works just fine but without holding it, it loosens itself which confuses me.

 

If the proper bushing is in its proper place, then follow the advice provided and use Lok-Tite on the bolt threads. If it still come loose with blue Lok-Tite, try red.