There's difference between "weight" and "mass". While weight is subjective, mass will remain constant for the object, as it derived from the volume of the object and its density. Speed and accelleration of the object are dependant on its mass/thrust ratio, so in order for capship to move as fast as a frigate it will have to acheave the same ratio (probably by stripping guns, armour and other usefull things that make it capship and replacing them with more engines).

Seeing as these ships are bigger, they need more power to go their life support and weapons systems, so their thrust would be nerfed in that respect.

Plus its a balance issue, players need to see the horrific metal death machine in time to do something about it otherwise the game would be too hard.