I wondered why this wasn't applied to suitcases to make them lighter and then common sense kicked in regarding just how much actual helium would be required to lift even an empty suitcase...
It's not even an issue of how much helium is needed; no amount of helium will make a typical suitcase buoyant.
Filling it with helium at ambient pressure wouldn't produce nearly enough lift, and increasing the pressure would make it heavier, not lighter. What's needed is not mass, but volume.
I feel like you're being deliberately obtuse. I think jianshen meant how big of a helium balloon you'd need, not how much helium you'd have to put inside the suit case.
Filling it with helium at ambient pressure wouldn't produce nearly enough lift, and increasing the pressure would make it heavier, not lighter. What's needed is not mass, but volume.