Long-range control demands a larger sensor system

Is modern warship size proportional to the much larger area its weapons and sensors can control?

Partly; reaching hundreds of miles requires sensors, computing, targeting data, power, and supporting equipment that impose their own space and weight.

Extending a combatant's reach to hundreds of miles requires a corresponding flow of targeting information. Sensors must gather the data and computers must process it into a usable form. That equipment adds weight and takes up space. Its electrical demand also has to be provided within the ship.