One of the things I find amusing in science fiction is that when spacecraft start getting his with enemy weapons, they might lose power. The warp engines go off line. The lights fail. At some point there is only enough power for life support, and that is about to go, and everyone will die unless someone can effect repairs before the last commercial.
But the gravity generators never go offline, even in ships that have been adrift in space for hundreds of years.
Maybe they use a method that doesn't require constant energy.
For example, the only hypothetical trick I ever took semi-seriously for generating gravity with less than the expected amount of mass involved a spinning macroscopic object composed of a Bose-Einstein condensate. Nevermind the tiny little problems of how to build such an object and start it spinning, but once it is spinning, it might just tend to keep spinning until you do something to stop it.
In all the Star Trek I've seen (almost 100% up to two years ago) I can recall gravity being a story point only once. I think it was the premiere of Enterprise, where Travis found a "sweet spot" (null gravity) on the ship where he'd go to relax, and said every ship had one.
There was also the opening action scene of ST6, with assassins disabling gravity aboard the target's ship and walking around with magnetic boots while everybody else floated helplessly.
That scene also showed that Klingon blood is a strangely bright purple, whereas it's been shown to be more like human blood in a few other scenes in other episodes/movies.
I did give it some thought, not much mind you, but, it went along the lines of, does it matter what the craft/ship weighs in space all that much?
Force equals mass times acceleration. The more mass a thing has, the more force is needed to cause a given amount of acceleration. And the amount of mass we're talking about to generate substantial gravity is huge.
You'd get some help from the fact that the mass can be a lot closer to you than most of Earth's mass is and some lower gravity level than Earth's might be acceptable, but, even adjusting that amount down by a factor of a few million (for a mass a few feet away instead of four thousand miles away), you're still left with the fact that a "1/few-million"-th of the Earth's mass is still several billion tons. A space shuttle without its fuel or boosters weighs about 86 tons. So, for a shuttle-sized ship to carry enough extra mass to generate anything near Earth's gravity, the ship's mass including the gravity system would be somewhere around a hundred million times higher, give or take a digit or two. And then so would the thrust it would need in order to make the same kinds of maneuvers. And that's without accounting for the mass of whatever you hope to produce that thrust with.
What if the hyperdence matter was made in ultra thin sheets at the sweet spot between thick enough to generate a gravitational field but thin enough to be manageable?
Things that massive and dense don't form sheets. They form spheres. Even if you originally hocus-pocus it into existence as a sheet, the first thing it will do is turn into a sphere.