"Windmeister"Zebra,
When manufacturers are using thicker barrels to increase accuracy of their rifles, it's not to add weight, that is a by product of what they are doing. They are adding stiffness (modulus) to their barrel. As you correctly surmise, it's about harmonics, and you can only combat harmonics in a few ways, adding thickness to increase stiffness is the cheapest and easiest way to do this, but the drawback is weight increase in the wrong end of the gun. I cannot think of any gun where you do not want the center of the mass close to your body, much easier to control.
The other solutions to increase barrel stiffness and/or accuracy are both time consuming and a bit of trial and error. One solution is sleeving the barrel in stiff materials like carbon fiber, which also have the benefit of being a different modulus, which harmonics do not want to propagate trough (going from one density to another) Tuning the barrel with a tuning device (small weight) this is time consuming and a round specific solution. Tensioning the barrel is another effective method of controlling harmonics as well as add overall stiffness.
The primary accuracy issue we are talking about here is harmonics, or waves causing nodes and anti nodes to form along the entire length of the barrel, and you cannot get rid of it completely. Only thing you can do is to minimize it, and/or force the nodes to form where you want them too.