Shipbucket

Keep in mind, what other countries considered unimaginable extremity in AA firepower, was the absolute minimum for American ships. All those AA guns, the ammo, the platforms and the directors high up, is going to add some weight.

It depends on where you put it. The Atlanta class had very narrow
hulls and limited deck space. The beam twin 5 inch turrets were replaced
in the follow - on Oakland class with quad 40mm AA, not because of any
weight problems, but rather because there was no other space for them.
On destroyers, the only way to add 40mm and radar was to place the
new AA on the second deck, and the radar at the top of the mast. To offset
the increased topweight, the destroyers had to eliminate either one 5 inch
gun mount or one set of torpedo tubes. If not, then the ship had a higher
center of gravity and would roll over (turn turtle) in heavy seas.
The destroyers also had limited space, so something had to be removed
just to clear some deck for the new 40mm. In the USN, only the Sumner and
Gearing class DD's were designed to carry 40mm AA guns, all others were
modified after commissioning.