I was thinking about this today< and it occured to me that the size/mass of the object being moved must bear on the power of the warp drive given that larger ships have engines that are proportional to them. Otherwise we might as well have all warp drive units looking more or less the same size on the ship.
Well, yeah; the bigger the ship, the bigger the warp bubble needs to be to surround the ship, and thus the more powerful the machinery needs to be to generate it. So I'd say it's more a function of the volume of the ship than its mass.
If you recall, Ds9 stated that creating a warp field around the station would lower it's overall mass (which allowed for thrusters to position the station at the mouth of the wormhole in a speedy manner).
This mechanism apparently takes place every time a warp field is created around the ship/station - which in effect easily explains 'jet fighter' type movements of large ships (which later on was apparently dropped for 'drama reason' - or as always - the writers forgetting (unintentionally or otherwise) what the technology can do).
Yes, that's the idea. And it kinda makes sense. Mass is essentially, for these purposes, a distortion in the fabric of spacetime. If you "flatten out" spacetime around an object, you effectively cancel out its mass. So you're warping (i.e. reshaping) spacetime, you're just warping it in the opposite way from how your ship's or station's mass does so, thereby cancelling it out.