Here is a rifle which actually is well balanced. It is both balanced on the shooters shoulder and has balanced recoil (essentially none). It's a Carl Gustav recoilless rifle and weighs about 32 lbs.
I can't think of any hunting rifles which are close to being mechanically balanced. The entire mass is in front of the shoulder and supported by the strength of the shooters hands and arms unless it's on a bipod or rest. Ether the torque moment required to hold and swing with rifle is easily within the strength limits of the shooter or it's not. That makes people call the rifle balanced or not.
I ripped muscles in both my shoulders four years ago and all of my rifles and pistols instantly became "unbalanced". As I healed they started returning to being "balanced" again. The first I could shoot again were my Carbon 15 rifle and a Browning 905 22short pistol. I'm mostly recovered now but my Pauza P50 (26 lb) 50 BMG semi-auto is still to heavy to hold on target offhand like I could before my injury. It's fine with a bipod.
In my opiniion there is no formula for a "balanced" rifle fired offhand. It's determined by the strength and abilities of the shooter. I have several rifles that I only shoot off bags or a bipod. The're too heavy to shoot offhand comfortably and introduce muscle shake if I try. It's not just the rilfe weight. it's the incremental weight times the distance from the stock which matters most. A 10 pound rifles with a 30" bull barrel will be harder to hold and swing than a 12 pound rifle with a 24" tapered barrel.
I would never add weight to the stock of a rifle. I won't carry pounds of extra weght for hours in the field to help me balance a rifle for less than a minute of shooting it. An underhook can keep the buttstock from sliding up the shoulder on long barrel rifles while adding very little weight. Our great-grandfathers knew that for their long muzzle loaders. If the barrel is so heavy I can't hold it up comfortably there are a lot of lightweight options like a bipod or shooting sticks or a sling to hold the left elbow up.
Benchrest rifles are a different story as weght distribution over the rest affects point of impact.