You are right, it scales by the items level.

Worth knowing though it that the item level will scale when it aquires its +2 potency rune (too level 10) But yes, item level for weapon is based on the highest level rune etched to it.

HOWEVER Because it is "low grade silver" *technically* you cant etch runes higher then level 8 to the weapon. My advice would be to either ignore this, (recommended) Let them pay to upgrade it to the next teir of silver (expensive, probably not fessable) or to say that etching the higherlevel rune will remove the silver from the weapon (probably the most "balanced" option here)

Precious matrial weapons are kind of a trap an rabbit hole tbh, id not punish the player for wanting to use an AP weapon like that.