Weapon Skills

A skill can be added to a weapon for a total of 8 times. Every time a skill is added onto a weapon, it will also gain a small damage bonus (around 1-4 depending on the weapon).

Types of Skills
There are a total of 16 different types of skills for a weapon. A weapon is limited to only 1 attribute skill, 2 attack radius skills,  and 1 rage skill

Cost to add Skills
The cost for adding skills is calculated by the following formula

Cost = (Blacksmith Type cost) x (Cost depending on which # of skill this is) x (Value of Weapon)

Item Level costs follow the following trend

For example, say you have a Wooden Hambard that's valued at 80 gold. Using the Spendthrift Smith (1.0x cost), the cost for adding a random 1st skill to the Wooden Hambard is only 8 gold. With the same Wooden Hambard, now you're trying to add a Lower Weight (L) by using the Dainty Smith (7.0x cost) as the 8th and final skill. The total cost for adding this skill would be (7.0) x (80) x (1.65) = 924 gold

How Rage is Calculated
Rage increases the overall damage regardless of the redness of a square (similar to power lock). The amount of damage increased is independent of the weapon's attack power (also similar to power lock). Rage damage increase follows this pattern:

It's impossible to take more than 49 damage and survive, so the maximum bonus damage increase that you can obtain from Rage is 32.

Since a lot of the weapon's redness square multiplier is around 0.4-0.6, averaging around 0.5, the rage skill can give you the equivalent from anywhere between +32 to +64 attack. Also, because the rage skill is independent of the redness of the square, weapons with a large attack radius will benefit more.

Rage is pretty useful in the beginning of the game when you need a bit more attack to defeat a boss. But stronger weapons in the later part of the game will actually benefit more from a Attack Bonus Up (S) than a Rage skill.

td;dr It's okay to use this skill on an early weapon (wooden sword or mace etc) but it's not a great skill overall.

Trivia

 * It's generally smarter to add the more expensive skills onto a weapon first. Due to multiplicative effects, the longer you wait to add an expensive skill, the more expensive the cost will be. Say you have a Halberd (value: 1200). Adding a fire attribute as the 1st skill using the Blackened Smith will cost 600 gold. Using the Blackened Smith as the 8th skill will cost 9900 gold.
 * The total cost of upgrading a weapon with a single element as skill 1, 2 range upgrades as skill 2 and 3, and Attack Power Up(S) as 4-8 will cost 11.9(Value of Weapon). This is one of the best ways to have a strong weapon on a budget