On my test site I:

1. Opened Shop in the Admin Console.

2. Entered Shipping Methods.

3. Created a new Shipping Method.

4. Labeled it Weight.

5. Set Enabled? to Yes.

6. Set Percentage of Weight to 5. Saved.

7. Went back to the site and edited a Product.

8. In the Shop tab of the Product I set the Is shipping required? field to Yes. Saved.

9. Edited a variant of the product.

10. Set the variant's weight to be 500. (Price is 150.) Saved.

11. Added the product to my cart.

12. In the dropdown box to select the shipping method Weight indicated 0.00.