Doubling GWM reduces average damage output.
I did some math to calculate how having a doubled GWM feat affects your chances to hit and your average damage output. I assumed that the PC was a single-classed fighter, starting with 18 STR and using their first ASI to get to 20 STR, and I assumed the enemy was always a monster whose defensive CR was equal to the PC's level. I also assumed that your homebrew weapon dealt 1d12 damage.
With these calculations, the necessary minimum roll to hit is remarkably consistent throughout the levels.
Without GWM, the fighter needs to roll at least a 7 to hit at early levels, and needs to roll an 8 to hit at most levels above level 9. Their average chance to hit on any given attack from levels 1-20 is about 63%, for an average damage output of 7.1 damage per round (11.35 dmg per hit).
With GWM, the roll to hit increases to to 12-13, and the average damage rises to 21.35 dmg per hit. The chance to hit drops to about 38%, but the increased damage outweighs that, so the average damage per round rises to about 8 damage per round.
With double GWM, the roll to hit further increases to 17-18, and the damage per hit rises to 31.35. However, the chance to hit drops to 12.75%. At this point, the drop in chance to hit outweighs the increase damage, and the average damage per round drops to 4 damage per round.
Even when the PC has advantage, doubling up on GWM significantly reduces their average damage per round.
These statistics mean the weapon is a little better than a +1 weapon in gameplay.
So what's the effect of these statistics in actual gameplay?
First, nobody will ever want to double up on GWM, since it cuts your average damage output roughly in half. I can maybe imagine a desperate situation where the PC would want to go for broke for extra damage, but that will be rare.
Second, you're granting half of the Great Weapon Master feat. As we can see from the stats, the boost in damage per round is approximately the same as a +1 weapon, at least under the assumed conditions. However, a player who would have taken the GWM feat might take an ASI for their attack stat instead, which is equivalent to a further +1 weapon, which you should consider.
Finally, hidden in these average statistics is the fact that this weapon will cause your combats to become more swingy. Instead of dealing a steady drip of damage, this PC will be useless most of the time, and suddenly deal a ton of damage every once in a while. As a DM, I find that rare occasions of "good" luck are much harder to deal with than more predictable situations. You'll have to decide how much swingy-ness you and your players are willing to tolerate.