Sounds like something is impeding the gas flow, either through the burners, most likely, or at the valve assembly. I would start by removing the burners and giving them a good cleaning. Put a staightened coat hanger through each tube to be sure nothing is blocking it. Then take a small brass brush, I have used an old tooth brush, and brush the tubes vertically, up and down, the entire length.
If its the valve assembly, it probably would have to be replaced, I guess. If cleaning the burners doesn't work, call Weber CS.
Paul