Before a hen even starts laying eggs she builds up extra fat in her pelvic region. I've butchered enough pullets, hens, cockerels, and roosters to clearly see this. This excess fat is what she mostly lives on if she goes broody. This way she can take care of the eggs instead of having to be off of the nest looking for food and water. A broody hen losing weight does not mean something is wrong, it means the system is working the way it should.
Eventually the hen will use up that excess fat. Different hens store different amounts of fat. Some hens come off of the nest to eat, drink, poop, and dust bathe more than others. There is no specific time limit for all hens for when that fat runs out. From what I've seen it is typically a few weeks longer than 3 weeks. I use 5 weeks when I'm determining what I'll do with a broody but that is a fairly safe arbitrary number. I like to be safe.
The vast majority of broody hens will break from being broody when that fat runs out. That's Mother Nature's way of protecting them if none hatch. With living animals you do not get guarantees, you don't know what will actually happen with one individual. While it is possible a hen could starve herself to death after that fat is used up it is really unlikely.
Why do we break them from being broody if we do not want them to hatch? Partly it is eggs. She will not start laying again until she replaces the fat she used up. The sooner you break her the sooner she starts laying again.
A broody hen can disrupt the dynamics of the flock. She is taking up a nest and her interactions with other chickens change. In a larger flock that's not a big deal but if you only have a small handful of chickens and a tiny coop that could become an issue.
A broody hen can cause you extra work managing them.
Personally I break them if I don't give them eggs to hatch, because of lost productivity and the extra work they cost me. Breaking her now might make your move go easier.
Good luck!
