The point is that creating the mass manipulating fields is not what the technology normal does, and requires modifications that take time. It is not something the UFP can do when ever they want to.
Picard wrote:
Mass manipulating things that are outside of normal boundaries of warp field.
Deja Q wrote: Q: This is obviously the result of a large celestial object passing through at near right angles to the plane of the star system. Probably a black hole.
DATA: Can you recommend a way to counter the effect?
Q: Simple. Change the gravitational constant of the universe.
LAFORGE: What?
Q: Change the gravitational constant of the universe, thereby altering the mass of the asteroid.
LAFORGE: Redefine gravity? How am I supposed to do that?
Q: You just do it. Where's that Doctor, anyway?
DATA: Geordi is trying to say that changing the gravitational constant of the universe is beyond our capabilities.
Q: Oh. In that case, never mind.
(Crusher enters)
Q: Ah, Doctor Crusher. I see Starfleet has shipped you back into exile.
DATA: Q says he has hurt his back.
CRUSHER: Ah ha. Well, if I didn't see it with my own eyes, I wouldn't believe it. According to this, he has classic back trauma. Muscle spasms.
Q: I've been under a lot of pressure lately. Family problems.
CRUSHER: Well. don't expect too much sympathy from me. You've been a pain in our backside often enough.
Q: Your bedside manner is admirable, Doctor. I'm sure your patients recover quickly just to get away from you.
LAFORGE: You know, this might work. We can't change the gravitational constant of the universe, but if we wrap a low level warp field around that moon, we could reduce its gravitational constant. Make it lighter so we can push it.
Q: Glad I could help. Ow. I think.
Deja Q wrote: PICARD: Indeed. Human or not, I want no part of you. We will deposit you at the first starbase. Let them deal with you.
Q: But I could be a valuable member of the team. I'm human, I can learn.
DATA: He has provided important theoretical guidance for Geordi's analysis of the Bre'el satellite, Captain.
TROI: It seems you have an advocate, Q.
DATA: I am merely stating a fact, Counsellor.
PICARD: Mister La Forge, your status?
LAFORGE [OC]: I've been putting together a programme to extend the forward lobe of the warp field. The field coils
Deja Q wrote: LAFORGE: Extending warp field forward.
PICARD [OC]: Engineering, is that the forward limit?
DATA: Yes, Captain. We are unable to encompass the entire moon.
PICARD [OC]: Do you recommend that we proceed?
Q: The two parts of the moon will have different inertial densities.
LAFORGE: Stand by, Captain. I can adjust the field symmetry to compensate.
Q: I doubt it.
LAFORGE: You don't know what this ship can do, Mister. Yes, Captain, I still believe it'll work. Increasing power and warp field and tractor beam.
Q: And if you're wrong, the moon will crumble due to subspace compression. Don't say I didn't warn you.
LAFORGE: Shut up, Q.
Q: I will not be spoken to in this manner!
LAFORGE: Data.
DATA: Q, I strongly suggest that you cooperate.
DATA: Inertial mass of the moon is decreasing to approximately two point five million metric tonnes.
LAFORGE: It's working. We can move it. Firing impulse engines.
Emissary wrote: DAX: It is no ordinary wormhole. My analysis suggests that it isn't even a natural phenomenon.
BASHIR: Not natural? You mean it was constructed?
DAX: It's very possible whoever made the Orbs also created this wormhole.
O'BRIEN: The Cardassians are leaving their position on a course toward the Denorios Belt.
KIRA: Mister O'Brien, what would it take to move this station to the mouth of the wormhole?
O'BRIEN: This isn't a starship, Major. We've got six working thrusters to power us and that's it. A hundred sixty million kilometre trip would take two months.
KIRA: It has to be there tomorrow.
O'BRIEN: That's not possible, sir.
KIRA: That wormhole might just reshape the future of this entire quadrant. The Bajorans have to stake a claim to it. And I have to admit that claim will be a lot stronger if there's a Federation presence to back it up.
DAX: Couldn't you modify the subspace field output of the deflector generators just enough to create a low-level field around the station?
O'BRIEN: So we could lower the inertial mass?
DAX: If you can make the station lighter, those six thrusters will be all the power we'd need.
O'BRIEN: This whole station could break apart like an egg if it doesn't work.
DAX: Even if it does work, we're still going to need help from Starfleet once we get there.
O'BRIEN: The Enterprise is still the nearest starship. They could reach us in two days.
DAX: We should advise Starfleet that we will require their assistance.
KIRA: You have Ops, Mister O'Brien. Lieutenant, you're with me.
DAX: Aye, sir.
KIRA: You too, Doc. Time to be a hero.
BASHIR: Yes, sir.
In "Emissary" they lower the inertial mass of the station and everything on it by modifying the deflector generators to create a sub-space field
In "Deja Q" they create a special program in order use a warp field to alter the gravitational constant of the moon. They would not have thought to use the warp field in that manner had Q not made his suggestion, and that tells us that they do not normally use warp fields to lower the gravitational constant of things normally.