Parameter scaling and infusions explained

The stat system works like this:
Weapons have a set of "parameters." This is the factor by which they scale with your stats. There are weapons that don't scale with stats (they'll have a - in the parameter slots) and therefore don't gain any damage beyond the weapon's own damage value. Other weapons will have a letter under the icon for one or more stats. Usually it'll be like B, C, D or E. Actually the range goes S, A, B, C, D, E, with S being the highest and E the lowest. I don't know why they chose an S.

They rank approximately like this...
S: super!
A: very high
B: pretty good
C: decent
D: weak
E: almost nothing

It's rare for a weapon to have A or S scaling in any stat. Most of them have C or D. If a weapon has D or E in a stat, it's generally not worth raising that stat for extra damage with this weapon. If it has C or higher, it's probably worth it. The parameters increase as you upgrade a weapon; the longsword starts with D/D in str/dex, but as you upgrade it, it'll eventually have C/D.

To see how much damage you gain from a weapon's scaling, look at it in your inventory and see what number is added to its base damage. If your longsword has 110 base damage and you have enough strength and dexterity for a combined 30 extra damage, it'll say 110 + 30. If there's a negative modifier (with red color), it typically means you don't meet the weapon's stat requirments.

Just like with boobs, there can be variation within one letter. It's possible to have two weapons with C scaling in the same stat where one has more than the other. If you compare these in the inventory screen, a blue letter indicates higher and a red indicates lower. A weapon with very high D scaling in a stat could gain almost as much from it as another weapon with very low C scaling.

Most weapons lean toward one stat or another and will go up one category in that stat over the course of upgrading it to the maximum. Some weapons have equal scaling in two stats and are colloquially called "quality" weapons because the infusion from Demon's Souls that gave a weapon equal scaling was called Quality. In Dark Souls III, that infusion is called Refined. Any weapon with equal str/dex scaling (high enough to matter; generally C/C) is thus called a quality weapon, even if it isn't actually infused with the Refined infusion.. which used to be called Quality infusion... hence the nickname.

Infusions work like this:
There's a number of different infusions you can apply to a weapon at the blacksmith. You need the right gem for each one, and some of the more advanced ones require that you first unlock the blacksmith's ability to do these infusions. Each infusion changes a weapon in some way, usually with regard to its damage and scaling parameters. You want to pick an infusion that best suits your build.

For instance, if you infuse a weapon with Heavy, it improves its strength scaling. Usually, these infusions reduce the weapon's base damage a little to compensate for this so that you do need to raise that stat in order to get good value out of the infusion. Some infusions also remove a weapon's scaling in exchange for higher base damage, like Raw, which is useful for builds that want to save stat points by staying at the minimum required to equip the weapon and therefore get more damage out of Raw than they would from their meager stat scaling.

Some infusions split the damage into physical and something else like the Fire and Deep infusions. Usually this removes the scaling, and splitting damage into two types means each attack gets reduced by two layers of the target's defense (e.g. its physical and fire resistance). To compensate for this, split damage infusions generally give a higher total damage. This is good for the same reasons as Raw: you get a higher total damage than an uninfused weapon, but without stat scaling. It can also be useful if you want to kill something that's vulnerable to fire or something.

Some weapons can't be infused. I guess it was deemed that they would be too powerful with infusion. Generally these are special weapons, ones that already have split damage or such high scaling that infusing them would be weird. For example, the Butcher Knife comes with A in strength even before upgrading, and ends up with S at +10, so it can't be infused because it's already essentially Heavy.

You also can't cast weapon buffs such as Lightning Blade on a weapon with a magical infusion like fire or lightning. Buff spells can otherwise improve your damage, but apparently they removed the ability to apply buffs on top of magical infusions. You can still buff physical infusions like Raw, Heavy, Refined etc. unless that particular weapon can't be buffed (usually the case with "magical" style weapons.)