Believe it or not wood sheds are heavier than metal sheds. You can use less building materials on a metal shed. A 10 x 10 metal shed is gonna weigh around 800-900 pounds. A 10 x 10 wood shed will weigh right around 1500 pounds.
A metal shed will weigh less than a wood shed for one it takes less material metal wood shed that is 8 x 8 is roughly going to weigh depending on how it's built between 200 - 800 pounds.
The weight of an 8x8 storage shed is going to vary by how good quality. and how thick the lumber is and what kind of roof material but in general between 600 to 800 lb is the weight of a 8x8 wood shed