Make sure you buy the starting weapons from the vendor outside the first boss in Cerasani Alley as if you progress to far into the story you can't go back to him.You will find normal weapons scattered throughout the game in chests. There is one that drops from an elite enemy. The rest can be bought from vendors throughout the game.
You will need to fully upgrade both vendors at Hotel Krat by finding the supply boxes and turning them in. One vendor sells two weapons when its fully upgraded the other sells the rusty cryptic vessel that unlocks Hermit's cave where there is a weapon located.
You can check your inventory to see which weapons you are missing.
0:00 3 Starting Weapons
0:34 Krat Police Baton
1:06 Salamander Dagger
2:16 Fire Axe
3:06 Boost Glaive
4:06 Big Papa Wrench
5:13 Blind Man's Double Sided Spear
6:09 Acidic Crystal Spear
7:21 Bone Cutting Sawblade
8:22 Dancer's Curved Sword
9:01 Exploding Pickaxe
9:54 Bramble Curved Sword
10:30 Electric Coil Stick
10:51 Clock Sword
11:50 Spear of Honor
13:09 Live Puppet's Axe
14:02 City Longspear
14:35 Master Chef's Knife
15:13 Coil Mjolnir
15:50 Military Shovel
16:37 Black Steel Cutter
17:35 Cursed Knight's Halberd
18:12 Tyrant Murders Dagger
18:31 Pistol Rock Drill
18:55 Circular Electric Chainsaw
19:40 Acidic Great Curved Sword
20:37 Carcass Crystal Axe