In Fire Emblem Three Houses there are numerous ways to upgrade your characters. You can upgrade them through certifications, you can teach them new tactics, and you can also purchase them new weapons. New weapons can be purchased from the Armory and they’ll cost gold each time you want to do so.
You can head to the Armory when viewing the schedule by heading into the Marketplace. Once in the Marketplace you will head into the Armory and see a host of different weapons to purchase. You can also sell your weapons that you have on hand that you don’t need any longer. Once in the Armory just select Sell instead of Buy and you can browse the available weapons in each character’s inventory that you can sell.
When selling weapons how much you’ll receive is directly correlated to how much durability a weapon has left. When purchasing new weapons for your units, make sure that they have the ability to wield the weapon. If you haven’t unlocked the Blacksmith in Fire Emblem Three Houses, this will be the best way to get weapons with durability or better quality.