The purpose of a weapon is to discourage, disable, or destroy. Attempting to wield a 7 foot steel blade with no weight, but 20 times the normal inertia is still a very, very bad idea. A swordsman using a standard long sword weighing 3.5 pounds (a little on the heavy side actually) will easily defeat you. Force = mass x acceleration. If you a wielding some with 20 times the mass (and 40 times the rotational inertia) you will always be way too slow andas you struggle to move your sword around. A common sledgehammer is around 10 pounds, try swinging one of those around quickly and you will find it impossible. This is not because of its weight, but its inertial.
You want to be able to accelerate your weapon at about 10 gees, sorry but no reference. The weight of the sword is thus only about 10% of the resistance due to inertia. Found an article subtitled Observations on the force exerted by a sword in swing that mentions: On average the test swords swung with 10.54m/s velocity and 117.19m/s^2 acceleration; (11.95 gees) -- so a little higher than my memory, but the testing conditions appear a bit artificial so maybe 10 gees is a better number anyway.
Unless you can get inertial compensators, lose the over-sized blade and get something that will actually be much more effective as a weapon. Now, suppose you are super strong, 20 times human strength. You still don't want that oversize weapon, you don't need to cleave an armored man in two to be effective. Imagine what Hercules could do with a standard longsword. Perhaps a two-handed greatsword would be better for Hercules because of the greater reach. But a 70 pound sword would just make Hercules slower than necessary. Due to great strength and skill Hercules might well find a heavier weapon more optimal than that a normal man might choose, but since Hercules would still favor speed over overkill power, the lightest weapon that preserves most of his speed is still his best choice. With his great strength any contact would be likely to kill or seriously wound any opponent.
Best weapon type depends upon type of combat. Mounted combat? Armored? Man on Man vs. Army vs. Army. One foe vs. multiple foes. No single weapon is ideal for all forms of combat or combat styles. If I had to select weapon without knowing combat type, I would probably select based on what fightsworks with my preferred combat style and experience and hope for the best.
Would anti-gravity help? A little - you don't have to lift the sword using your muscles so you would tire at a lower rate. How does antigravity work. Does it just means that Earth gravity is cancelled or does it cancel gravity from the sun, the rest of the galaxy, etc. Since these accelerations are multiple orders of magnitude less than 1 gee, you can ignore their effect and in fact do so every day.
How would an inertial compensator work. If it just cancels all or most of the inertia, your big sword now hits like a small sword because it has also lost momentum and kinetic energy. Thrusting attacks would still be mostly effective as they are less dependent on the inertial of the weapon. If your inertial compensator is smart enough to restore inertial just before impact or only compensate for inertial changes supplied via the hilt you would suddenly have a more effective weapon.
Adjustable inertial compensation would actually be pretty useful as you could set the mass of the sword based on combat conditions, and the extra reach would often be useful. You would not want to eliminate mass entirely as this would create a weapon with very poor balance, i.e., contact will tend to wrest it out of your hand.
Given the high tech levels required, one has to wonder why you would want to use a sword though. The only thing I could thing of beyond personal ego or fantasy role-playing was to assume you might be able to sneak in the tech in a setting similar to Ranks of Bronze by David Weber.
