OK, Larry, short course.
Weight determines the muscle effort expended to carry and lift and hold the gun. Teeter-totter balance determines on an individual basis the % of weight carried by each hand. MOI at teeter-totter balance determines the swing effort needed to make the gun point in a different direction while uncounted. MOI at butt determines the swing effort needed to change the direction the gun points after mounting. MOI at CG must be measured and MOI at butt can be calculated once MOI at CG is known. Balance at CG is determined with a "fulcrum" type pivot and tape measure. Weight is taken from a scale.
There is no magic "balance". Guns are static/fixed objects and do not change dynamic characteristic when in motion. The concept of a "balance" that sums the four handling characteristics is fine subjectively, but does not compute objectively. Useful information subjectively would depend on calibration between two shooters.
Most shooters will be enthralled with the handling of a British pattern game gun (6 1/2#, 4 1/2" CG to trigger, 1.45 uncounted swing effort, and 6.4 mounted swing effort). MOST PEOPLE WILL NOT SHOOT THERE BEST WITH SUCH A SET OF HANDLING CHARACTERISTICS. Most will shoot better with a unmounted swing effort of 1.8 or more and a mounted swing effort of 7.5 or more.
There is no point in harnessing yourself to a gun that requires so little swing effort that you can't easily control it (twitchy mother). Likewise, don't try to shoot a gun that requires so much swing effort that it tires you before you are done shooting (numb, to quote our British cousins).
Weight must attenuate recoil to your comfort and must not tire you prematurely.
Balance must be to your requirement. If you find yourself sliding your front hand around on the forearm after mounting, you may be sure the balance location for that gun does not suit you.
Questions?
DDA
