A gravity mage is someone intrinsically able to alter the gravitational mass of objects, without affecting their inertial mass.
They are able to do so only to objects they touch, and when they change the G-mass of something, an equal and opposite change occurs to their own G-mass. This change is not the permanent - the G-mass 'wants' to return to its original object. So, the moment it is done, G-mass begins to move back to where it came from. However, depending on their skill and strength, the mages can stop this for a time, though even they can't stop a minuscule trickle back to the source, like small holes being made in a dam slowly, until a point comes where the dam breaks and the G-mass "floods" back to its original source. Anywhere between 5% - 30% of the mass is lost before the big return, depending on the skill of the mage. This big return generally happens within half an hour for an average mage, but skilled mages can make their alterations last for up-to 6 hours.
A mage cannot reduce their own G-mass to 0,or even that of another object, though stronger and more skilled mages can come close, but it is a tedious process that tires them greatly. They can, however, make themselves as heavy as they like. A gravity mage who does not express caution will soon find most of their bones broken in an accident.
However, they CAN get around these limitations: by altering another object. Even a moderately skilled mage can alter two objects simultaneously. This essentially allows them to transfer G-mass from one object to another. Less skilled mages can do this in stages, by altering one object first, then oppositely altering the other, repeatedly until the desired result is produced.
Altering too many objects can cause a problem. Different objects lose G-mass at different rates, and a mage may inadvertently give more attention to a certain object over another. This can cause too much change suddenly in their own body, which can be fatal. So only very experienced mages attempt something too complex.
What can be the applications of this power?
Already, I believe they will be used in tandem with siege weaponry - making very heavy rocks very light to throw them over a large distance, and then letting the mass return once it is over the enemy castle (though is the last part even necessary? As the inertial mass is unchanged, I believe it would apply the same force and thus cause the same destruction regardless. It WOULD fall faster though, so perhaps the increase in kinetic energy is enough of a danger). They will also be powerful assassins who can easily make structures collapse or drop heavy objects on people, and they will be useful when carrying heavy loads up mountains, for instance.
Some limitations:
They can only alter what they are touching. However, once they have altered it, they can let the G-mass return whenever they want, by not resisting it any longer. So while they can only cause a change in very close range, they can potentially reverse that change prematurely whenever they want.
They are limited by the magnitude of the changes made. The rate at which they tire, both physically and mentally, is directly related to how many kilograms of G-mass have they displaced, and how quick they have displaced it. A mage of the same power can either displace 50 Kg in a minute or two tons over multiple hours. However, in practice the latter is more tiring as the G-mass that they have already displaced (twice, as they had to put all the extra mass somewhere) would be pressing harder and harder to return to its original source.
They are not abundant. They are not present in large enough amounts so as to be readily available when something needs done, especially for civilians. This is in part due to the extermination of all mages other than a certain kind, that is being carried out by a large warmongering empire at the time. So most G-mages are either in hiding, or in an army fighting against the murderous empire.
With these limitations, what larger scale things would gravity mages be able to achieve?
(By larger scale, I mean something other than the immediate personal level or team level. For instance, if trained well, they would be amazing fighters, as they can not only alter their own mass but also that of their enemy, whenever they want. If you allow one to touch you, they can not only disorient you once, but tactically undo their changes a bit at time. However, I consider this small scale application. Examples of a larger scale application are what I gave a bit earlier)