In order to compare the weights, let's check the formula for the weight force between two objects:
Where G is the gravitational constant, M1 and M2 are the masses and d is the distance between them
We can see that the distance is in the denominator and it's squared.
That means if the distance doubles, the force will be reduced by a factor of 4.
The distance from the debris if it was on Earth is one radius, so the actual distance is twice the distance that it would be on Earth.
Therefore the weight of this debris is 4 times smaller than its weight on Earth.