of course we know that. not the exact numbers, but we know it is heavyweight. but the main problem here would be the structural integrety of the hull with the heavy weight fore and aft, that gives problems here. these systems might fit on the ship, but not in this arrangement.
Mate you have no evidence to back any of those statements. The weight of the turrets and their barbettes is huge. Solid thick steel for armour is much heavier than thin aluminium aerostructure and rocket fuels. As to the weight balance the weight of the SAGE system replacing the forward two turrets is far more than even a bunch of rockets.
This is what a SAGE building looks like:
It more than replaces the weight of two turrets compared to a rack of launchers and a big hangar to maintain Alaska class CG. Even without the weight of the computer's massive cooling system and the HMI the SAGE's FSQ-7 is the same as 40 BOMRAC missiles. Since each SAGE has two computers and one would assume around twice as much weight forward as aft to balance the turrets that is SAGE forward, 40 missiles aft. Real numbers not just pixel impressions.