I think the developers made a mistake: they are offering a discount on materials only for levels 6, 7, and 8 of the new upgrade. The problem is that after the discount, they display the same number of materials normally required to upgrade the weapon. Normally, level 6 requires 6 materials, and levels 7 and 8 require 10 materials. In the image, you can see that they listed the pre-discount cost as 7 materials for level 6, 9 materials for level 7, and 13 materials for level 10.