Wouldn't it be more fun if it dealt more damage, though? Don't tell me that a straight sword which weighs as much as a fully grown large half-orc wouldn't do some real damage if you were strong enough to use it.
But how strong should you have to be able to wield that?
That means just by the weapon alone you are encumbered with 20 strength.
I don't think a 20 strength character would be able to swing it fast enough to hit easily, so maybe it takes two attacks to use and hits at disadvantage?
I actually like that idea for a separate custom magic item!
Scythe of Heavy Deeds
This +1 scythe always deals a base of 2d4 damage and weighs 10 lbs, even when sized for larger or smaller creatures, but grows heavier with the burden of use. Each time the scythe strikes a killing blow against a living creature with an intelligence score of 3 or greater, the scythe's weight increases by 1 lb. Every 5 lbs of additional weight increases the damage dice of the weapon by an additional 1d4 damage. If the scythe remains unused for more than 24 hours, the weight resets, and the additional damage dice are lost.
There should probably be a max damage, or your player could eventually do 75d4 damage just so long as it's used in battle once a day. As stated, it doesn't even need to kill anything during that time, so spar once a day, and in times of war get a ridiculous amount of damage.
Admittedly, it gets unusable at 301 pounds so you have to let it reset then.
EDIT:I just watched the first episodes of Saga of Tanya the Evil.
How about a cursed weapon that attaches to their hand that does 0 damage unless they pray to whichever God they and their allies least like?