This video showcases all weapons and their upgrades in Monster Hunter World. There are 421 unique weapon designs!
Might this be a record? There are 14 different weapons, each has a few upgrade trees with 1-2 weapon designs per tree. It comes down to roughly 30 design variants per weapon!

This video shows them in the same order as the in-game list (timeline below). Weapon upgrades can be crafted at the Smithy in Astera. All you need are monster materials which are acquired by slaying large monsters. Each monster unlocks new weapon upgrade trees.

TIMELINE - ALL WEAPON UPGRADES:

#1 - Great Sword - 0:05
#2 - Long Sword - 1:16
#3 - Sword & Shield - 2:06
#4 - Dual Blades - 3:16
#5 - Hammer - 4:20
#6 - Hunting Horn - 5:24
#7 - Lance - 6:16
#8 - Gunlance - 7:08
#9 - Switch Axe - 8:06
#10 - Charge Blade - 9:02
#11 - Insect Glaive - 9:58
#12 - Light Bowgun - 10:50
#13 - Heavy Bowgun - 11:58
#14 - Bow - 13:14