yes a heavy barrel is better when shooting lots of rounds. it also adds more over all weight which means less movement and recoil which helps with accuracy. the Savage 10 and Remington 700 both come with heavy barrels for $823 or less.
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when I was talking about the model 10 and 700 those were the versions I was speaking about. I only mentioned the Savage Axis to show that you don't need to drop lots of cash for accuracy. there's always a better tool for the job and the heavy barreled rifles are much better for lots of long distance shooting.