Take a look at weapon mounts. Light Cruisers have weapons that are 33% more powerful right off the bat (assuming you use the mount

). This is what allows them to so easily overpower anything smaller. Battleships have weapon mounts that make their weapons 50% more powerful than those of a Destroyer, or 28% more powerful than those of any Cruiser. This makes bigger ships much more powerful by default. That, and ships do not start getting slower in combat until Dreadnoughts, and just 1 speed slower on the game map with Battleships. Why ever use small ships when much more powerful ones are available?
Also, the Escort is a horrible hull for a warship. 60% of its space is used up just for C&C and engines! Add CS and ECM, that uses up 73% of the space! On a LC, those comps take up only 27.5% of the hull. Bigger ship hulls are in general much more efficient than small hulls (save Cruisers vs. Light Crusier, which is just slightly more efficient; and possibly the Baseship if speed is important, though that is not an issue of effeciency).