You would not roll the superiority die twice
The section on "Critical Hits" states:
When you score a critical hit, you get to roll extra dice for the attack's damage against the target. Roll all of the attack's damage dice twice and add them together.
The Sweeping Attack Maneuver states:
When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.
The Maneuver uses the phrase "with the same attack"; I agree with MisterB that this means that you are not making a new attack but I also believe it does means that the superiority die's damage is considered part of the original attack's damage.
Thus it would appear that you do roll the die twice; however, the critical hit section says that the damage you double is "against the target" (your original target). The second creature you are hitting with this attack is a new target and so the damage that comes from the superiority die would not double.
This is slightly supported by Jeremy Crawford's now unofficial ruling on critically striking with the green-flame blade spell:
Q. If you critically hit with the attack part of Green Flame Blade, and are greater than level 5, do you roll extra dmg against the 2nd target?
A. The splash damage of green-flame blade isn't affected by the attack critting. Think of the attack as process X & the splash damage as Y.
Here he uses a different line of reasoning for why the damage is not doubled, but it is a similar situation.