Why high speed consumed so much displacement

Why did the Iowa class need so much more displacement than the South Dakota class for roughly six additional knots?

Sustained speed requires larger machinery and fuel capacity plus a longer, carefully balanced hull, all while preserving armor and gunnery stability.

Sustained high speed demands far more than a simple increase in installed horsepower. Machinery, fuel, hull length, structural balance, and weight distribution all grow together. The Iowa class used roughly ten thousand additional tons over the South Dakotas to gain about six knots while retaining heavy armor. A fast battleship must remain a stable gun platform as well as a powerful engine installation.