You can do this by simply progressing through the story, collecting materials from the monsters you defeat, and selling them to the Smithy so you can craft better weapons. But you can also get amazing weapons from NPCs if you interact with them, and buy decent ones from the Exchange Shop with Memory Shards.
Method #1: Crafting Them In The Smithy
The most effective method of getting stronger weapons is through crafting them in the Smithy with the materials you gather from monsters. To unlock stronger weapons, you must first defeat stronger NPCs. This means you’ll have to play through the Main Story Quests to unlock more map zones and higher-level monsters. The materials dropped by regular monsters are random, so just try to eliminate as many monsters as you can if you want to craft stronger weapons. TIP: You can visit this amazing database by Meowdb to see which materials are required to craft a specific weapon.
Method #2: Buying/Taking Them From NPCs
You can obtain weapons by either buying them from Wealth NPCs, or taking them from Fame and Power NPCs. Here’s the list of actions you need to take for each NPC depending on their alignment: TIP: You can also check which NPCs you can get Weapons from the same database linked above, so feel free to check it out!
Method #3: Buying Weapons From The Exchange Shop
The only other consistent way for you to obtain stronger Weapons is to buy them from the Memory Shard Exchange Shop. Here, you can buy the Stamp Series weapons. They are all Level 20 weapons that’ll make great stopgaps in the early game until you obtain stronger weapons via crafting or talking to NPCs. TIP: These weapons cost 50 Memory Shards each, and provide you the same buff: granting your units a 20% chance to recover 1 BP at the start of every battle. This buff doesn’t stack with other buffs of the same type though, so make sure to check what buffs your other equipment pieces have so they don’t overlap with your weapon’s buff.