When you upgrade artifacts by clicking the upgrade button, it will start at "certain" then advance through, "high", "medium", etc. When you advance between stages, like from "certain" to "medium" it will add a level for each success, being granted a new substat for every 4 levels. A weapon in the "certain" stage starts at 1 and levels up with each successful upgrade until reaching the "high" stage, which is level 4 and later the "medium" stage is level 8. This is different than the star rating or rank, which, as @glizdazla noted, cannot be changed that I know of.