Imagine Earth has been a tenth as massive as it is now, does it makes sense for warriors in the medieval period to carry bladed weapon bigger than themselves? for this purpose we have to assume no change in our physiology. The only criteria for bladed weapon is that the total surface area must be greater than or equal to the entire surface of an average adult man's skin.
It's not that you can't lift it, it's that you can't maneuver the blade at all. Your average medieval arming sword has a mass of about 1kg. Say you now ramp that up to a 10kg blade. It has the same weight as before, so you can carry it around easily enough, but as soon as you try to swing it, you're going to find that 1) you can't get it up to speed easily, and 2) once you have gotten it up to speed, you can't stop it. And when your extremely slow strike inevitably misses, you'll be very off-balance and wide open for a return attack from someone wielding a more reasonably-sized weapon. Imagine swinging a 2kg sledgehammer like a baseball bat, then needing to stop it mid-swing to block an incoming blow with it. Now imagine trying to do that with something with five times the mass or more.
And from a fitness perspective, trying to wield a weapon that massive is going to exhaust your warriors way too quickly to be practical. Speaking from my own experience with SCA armored combat, even the most physically fit fighters need a breather after more than a few minutes of continuous fighting and they'll be done for the day after a couple hours of intermittent fighting. And that's swinging rattan weapons that maybe mass 2kg or so at most. Ramp the weapons up to the size you're talking about, and your warriors will be in noodle-arms territory in minutes, no matter how fit they are. The human arm and body simply hasn't evolved to put out the level of energy needed for any extended length of time.
Other answers have focused on the force needed to move it, but it's a matter not only of force, but torque. Doubling the length of a weapon while keeping the width and thickness constant doubles both the mass and the lever arm, making the torque four times as large. And less gravity also means you weigh less, so your body is less of a counterweight, and you have less friction to brace yourself.
The problem in a setting with low gravity isn't the weight of the weapon so much as it is the weight of the user. Imagine if you weighed 1/10th your usual weight, and you're trying to swing a gigantic beast of a weapon. Would you be swinging the weapon around, or would the weapon be swinging you? With a normal weapon (i.e. normal Earth-sized weapons), the user can swing them any which way he wants, because the weapon is light enough that the center of gravity is still the user. If your weapon weighed as much as you, or more than you, the center of gravity would either be the weapon, making it difficult to use in combat. There is one way to deal with this problem.
By wearing heavy armor all over their body, your men would be able to increase their mass and bring the center of gravity closer to their bodies so that they aren't being swung around by their own weapons. And before you say it: full-body armor isn't nearly as straining as it seems. People in the real world can do cart wheels and even do rock climbing without much issue because the weight is dispersed all over your entire body.
And I know you haven't asked for it, but low gravity would cause all sorts of changes to Earth besides warfare. For one, our gravity is part of what keeps our atmosphere on the planet. And depending on whether the moon's mass was also affected, our orbit around the sun and the tides might also be different, causing great changes to the ecosystem. Judging by the fact that human physiology is not affected by this, though, I reckon you'd be able to handwave the issue through some magic or some other similar thing.
No, this will not work.
The mass of the sword will stay the same, even if the weight changes, and so it will be just as hard to build up momentum as in the normal amount of gravity. Once you have finally used a lot of energy to swing the blade around, it will take the same amount of energy to stop it. Your enemy can just avoid that attack easily and off you with a much more reasonably sized sword.
At least you might be able to distract them with the sight of a man lugging around a 10kg sword on a battlefield.
Sure, they make great shields
If everything weighs 1/10th as much, yet human strength remains the same (and object density does as well) than that means arrows have a lot further reach alongside all ranged projectiles. And, since ranged projectiles are superior when you're dealing with unarmored infantry, that means the range game is deadlier at farther range, so defense is more important.
A sword larger than a human seems like a great shield. You'd have to weld a grip to either side of the broad blade for improved handling, so when your infantry charged, they could hold the blade like a shield, and then shift to gripping the hilt and swinging the swords around.
Also, remember, the strength of a sword comes in part from their weight. Which means that if you've got little frogstickers swirling around, they'd still be fine for thrusts, but slashing will be a lot harder.