That really has nothing at all to do with hunting, since those rifles aren't carried at all, and winning is often measured in fractions of an inchIf the weight of the barrel was irrelevant (or the least relevant factor) why would the National Bench Rest Shooters Association classify bench rest rifles by weight?
Such a classification system suggests the weight of a barrel is so relevant to the accuracy of a rifle that it must be accounted for in bench rest competition.
Many sports have weight limits for different divisions to assure the equipment is the same, and not because one weight is "better"