Barring the fact that this is dangerously close to gravity manipulation, which is banned, there's the issue that it's still way too easy to kill someone with it. She has to touch someone's head, make their skull way about a million times more than their spine can support, and even when their head drops past her finger, they're dead. 

Not to mention that, since f=ma, if your character lowers their mass to move faster, they're still hitting with the same amount of force. In other words, near light-speed, your character hits with the same force while being impossible to hit back. Your character could also dodge any attacks thrown at them. Also, the ramifications of moving that quickly would utterly destroy them, as we already touched on with Didact's speedster, who runs into the same problems at far lesser speeds.

Her being able to increase her own mass means she can become pretty much invulnerable whenever she needs to, and there's not even the drawback of her falling through the floor because she can increase the mass of the floor beneath her as well.

Objects being weightless while she's carrying them is a nonissue. Again, run past someone with a car/aircraft carrier/family of rhinoceroses and drop it on them. She's gone because she can move so absurdly fast before they know what's happened. She could stop bullets as they hit her, do the same with punches, any objects, etc. Given that she can move at light speed, her being limited to things she can touch isn't that much of a drawback.

Your character is incredibly powerful and I don't see any way this power will work. I think a new one would be better.