Some weapons seem to have a lot of added stats such as Atk Spd, Dex, etc.

(I obviously do not own that)
How do weapons get those extra bonuses? I had assumed that it had something to do with Smelting but if someone could clarify this, it'd be much appreciated.
Also as a follow up question, how does the enhancement mats affect the enhanced weapon? Do I need higher level weapon mats + higher grade (please specify how much a high grade is) to enhance efficiently?