As others have mentioned, thicker "heavy barrels" have less flex, so they don't whip as much with the bullet in the bore. The extra weight of the rifle also increases shootability and shifts the balance point of the rifle towards the muzzle (or actually towards the middle of the bbl, but it moves it towards the muzzle from previous position), so the muzzle doesn't hop as much on a shot, and is easier to stabilize while aiming.