Any thickness of barrel can be made to shoot with hand loads. Depending on the quality of the barrel and the quality of the loads. When searching for the accuracy node one is, keeping all other factors in control form of the experiment, search for the right powder charge. One is looking for a bullet to exit the barrel in the part of the sine wave when the barrel has flexed upward, paused, bullet exits, barrel rebounds downward. That is the accuracy node.
You may have a powder charge spread, especially in a long magnum, 1.0 gr below to 1.0 gr above the "sweet spot" and the rifle still shoots well. Heavy barrels allow longer shot strings before the barrel heats up and harmonics change. But even the thinnest contour can still shoot sub MOA if the barrel is allowed to cool. Obviously ambient air temperature is a factor.
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