Roy,
Its only a few things it could be. Only thing that would cause a carb to bind is cable, throttle, slide, and needle. On the 350x, that includes all of linkage from the cable to the arm that raises the slide.
It makes no sense why it wouldnt happen when running. The air moving isnt going to make a carb bind up at 1/4 throttle. Check to make sure the cable is routed correctly and it isnt catching on the trips or any other wires/cables.
Also check out the throttle. Are the grips stopping the throttle from returning at all? Did you just put new grips on?
Mike
1986 Tri-z
1985 250r
1985 200s
1985 70[/SIZE]