There are many reasons why Navy ships are big, but a few merit special note. The considerations listed here apply to the whole gamut of warship types of the Industrial Age, from the Royal Navy's old sailing ships of the line to the most modern aircraft carriers and cruisers.
Almost all combatant ships are the first stage of the various weapon systems found aboard them. That is, the ships are the platforms which carry the heavy machines that constitute the second stages of the weapon systems. The second stages those which deliver the warhead to the target area are guns or airplanes or missiles. Because these second-stage machines are usually big and bulky, the ship that carries them is itself necessarily big and bulky. And, generally speaking, bigger guns and bigger planes hence bigger ships have been needed to put more range into the second stage.
The direction and guidance of the weapon systems of the Industrial Age are imprecise relative to more modern weapons. Thus many pieces of ordnance (such as shells, bombs, missiles, mines, and torpedoes) are required to ensure target destruction. Moreover, ships expend imprecise ordnance rapidly when engaged in combat, and neither returning to port nor replenishing daily underway is desirable during hostilities. Thus, large magazines are required, and large magazines entail large ships. As well, large replenishment ships are required to carry more ammunition to the battle areas.
Ships must go deep into harm's way because most current weapons have limited range. Thus, ships require excellent speed, superior maneuverability, and elaborate damage control measures, including extensive compartmentation. All these add more size and weight to ships already large.
And cost: the propulsion power, maneuverability, and size are dearly paid for. Consequently, Industrial Age warships are built with as much combat capacity as possible.
In addition to making optimal use of ship size, concentrating weaponry into one large ship facilitates communications. For Industrial Age warships, intra-ship boatswain's pipes, bugles, sound-powered phone, and FM headsets are more reliable forms of communication than ship-to-ship signal flags, semaphore, flashing light, CW Morse, and UHF. If the same amount of firepower is distributed among many different ships, it is difficult to control. Put another way, given Industrial Age communications constraints, it is easier to concentrate fire from one Industrial ship than from many.
Of course, such ships required many people to maintain, operate, and protect them. large ships, large crews. And large crews need more space for messing and berthing.
The tendency, then, is to make Industrial Age ships very large indeed and to load them with expensive, complex weapon systems and many people. These ships are formidable, deadly, big, and valuable.