Question about refining melee weapons?

Sadism - Lost City

Ok, so I know that when you refine melee weapons, you increase their Physical Attack. I also know that depending on the grade of the weapon, the more Physical Attack boost it gets. (ie. low grade, mid grade, high grade) Also, depending on the number of successful refines, the greater the multiplier.

But my question is how much extra physical attack do melee weapons get? Do each type of melee weapon get the same addition to physical attacks? (ie. do fists get the same physical attack boost as an Axe?)

Also, if anyone has a general idea of which levels are considered low, mid, and high grades, that would be helpful. Oh, and how much of a boost in physical attack are we looking at? I can only find out that mid grade heavy armor gets a +15HP.

Thanks in advance for your input on this matter.