Weapons can be upgraded at the Home Base area by speaking with Murasame. She is the masked female vendor standing in front of the vault door. She will allow you to upgrade your weapons. Weapon upgrades can be done if you’ve got Haze currency and Queen’s Metals like Iron, Steel, Titanium, and Tungsten.
Weapon upgrades in Code Vein make them stronger, boosting physical stats like power ratings for the physical damage they can inflict. Upgrading a weapon for the first time will make it a +1 and will continue to increase as you upgrade the weapon. As you upgrade weapons more and more, it will cost more and more haze and materials to perform the upgrade.
Weapons can be leveled up and upgraded to level 10 but so can your Blood Veils. You can level up each individual Blood Veil in the same way that you do weapons and you’ll do it at the same vendor. Along the way you’ll use different types of Queen’s Metals to perform the upgrades while the price in terms of haze will get higher as well. Haze can be found out in the world in the form of capsules that can be stored and then used to gain haze. Or, you can collect haze outright from defeating enemies.
Queen’s Metal on the other hand needs to be tracked down in specific parts of the story or certain depths levels.