Depends on what type of mirror that is. I am going to assume this is a plain mirror (from the phrase), which means the height and width of the object and image is exactly the same.
The weight will be 1/6 of whatever it is on Earth.
Explanation:
Remember F=ma
If the acceleration decreases by a factor of 6 while the mass stays constant, you can see the force (the weight) will also decrease by the same factor.