Neither I nor a friend of mine have Weber grills, however we did have the similar problem.

The burners didn't seem to heat very much, not a lot of flame.  If we didn't turn the tank on completely but just cracked the valve we got the flames and heat you would expect.  Turning on the tank full the flames and resulting heat weren't sufficient to cook a hotdog.

Now I open the burner valve, crack open the tank and light the burner.  Works, probably a problem with the regulator.