Alchemy Merging
Although I put this at base level 40 this is probably available as soon as you join a guild. Alchemy merging, or "Refine Enhancement", a less spoken feature of the game which allows you to enhance the Refine Atk and Refine MAtk of weapons and accessories as long as they are refined to a certain point. This may be done in your guild by speaking to the Alchemy Merging and Artifact NPC's.
As this only affects Refine Atk/MAtk only this is more of a PvP feature so you're not expected to do this if you don't participate in PvP.
Location of the two Alchemy Merging NPC's
There are two parts to the process. First, you need to procure Enhancing Essence. Then you spend this essence to increase the level of your refine enhancement. This essence may be obtained a few ways.
The first, is to spend Honor Proofs on them at the vending machine in your guild. Unless you have a huge surplus of Honor Proof you should avoid this method because buying praying pack cards is much more important.
Another way to obtain this essence without spending honor proofs is through Alchemy Merging.
Alchemy Merging
Speak to Vagrant Alchemist Spike, the NPC with the big "Alchemy Merging" sign over his head and select Alchemy Merging.
On the right of this screen you'll see three Enhancing Essences to choose from, with Enhancing Essence I chosen by default. In the center you'll see the item you've selected, a range of numbers indicating how many Enhancing Essences you'll get out of the process, and the percentage of auxiliary and main donation made towards this goal. On the bottom are two lists of materials, auxiliaries and main ingredients which you'll use to create these Enhancing Essences.
In order to create them you must use enough Auxiliary and main ingredients to fill up both sides to 100%. Once you do this you may click craft to spend those materials and 10,000 zeny to create some Enhancing Essences. Crafting higher level Enhancing Essences require higher level materials so keep that in mind.
A case where I've used 2 Cursed Rubies and 118 Jellopy. You cannot craft until both the blue (auxiliary) and purple (main ingredient) gauges reach 100%
Refine Enhance
To begin spending these Enhancing Essences speak to the NPC next to alchemy merging, Mr Dragon, and select Refine Enhance.
Refine Enhance for my weapons
Refine enhance for my accessories
Note that this already requires Enhancement Essence II at level 3
To enhance simply select either Weapon or Accessory on the top right, then click Enhance if you have enough Enhancing Essences, the process will always succeed.
Once you've applied some enhancements you can switch the bonus to physical or magic attack however you see fit whenever you like. Note that the accessory enhancement applies to both accessories so upgrading this first is most likely your best move here, at least to the Intermediate tier.
Note that at current, it states that my Weapon enhancement is "Weapons - Basic". This is because I am in the Basic tier. the first of five (5) tiers. The bonuses get much larger at higher tiers, but those higher tiers are not activated unless your weapons and accessories reach a certain refine level. The tiers according to the help text are:
Basic - Effective at refine +1
Intermediate - Effective at refine +5
Advanced - Effective at refine +9
Top - Effective at refine +13
Ultimate - Effective at refine +13
This means most PvE players should expect to eventually get this to Advanced since more of us are always running around with +10 weapons, though accessories usually take longer since several are very, very expensive. Again, if you don't PvP this is probably an extremely low priority but know it's here and use it when you find yourself overloaded with materials you can't sell or want a little bit more true damage.