Weapons level up the more you use them in The First Descendant and that is what is referred to as Weapon Proficiency in The First Descendant. Each armament will have a proficiency bar that fills up over time.
It’s one of the core systems of helping your characters grow more powerful over the course of the game. However, the mechanic is not something that the game properly explains to those who are new to The First Descendant.
How does Weapon Proficiency work in The First Descendant

Weapon Proficiency represents the level of a weapon and the amount of time that you have used it during your playthrough. You can check the Proficiency of a weapon by going to your inventory and hovering over it.
The max Proficiency level that you can reach is 40 but you can reset the level by using a Crystallization Catalyst which will help you insert different Moduel Slot types to help manage your capacity limits better.
Increasing a weapon’s proficiency to the max will help increase its module capacity as well so make sure you are consistently leveling up your Ultimates.
Best way to increase Weapon Proficiency in The First Descendant

The best way to increase weapon proficiency is by taking down enemies and completing missions. Special Operation missions in particular are one great way of farming Weapon and Descendant XP.
However, there is one mission that will let your take both your Descendant and Weapon to Level 40 in under an hour if you keep repeating it. This is a Void Fragment mission found in the Fallen Ark region of The Fortress and you will need a Bunny or a Sharen in your party to keep completing it.
Bunny will be the best choice and the reason why this XP farm is one of the best in the game is the fact that enemies spawn in close proximity once the quest begins. All a Bunny needs to do is to pick a spot and keep double jumping there and she will be able to take out all the enemies while hitting the reactor at the same time.
It’s currently one of the fastest ways of earning both Weapon and Descendant XP. Just make sure that World Map is set to hard when starting the mission.