It's interesting, contemplating how the development of weaponry would differ if our primary enemy as a species wasn't ourselves. If monsters the size of elephants were the norm rather than a frightening rarity, we'd no doubt have a whole slew of different weapons. We've developed large weapons for as long as we've been able, but no doubt we'd have put extra effort in with suitable foes to motivate us.
Ludicrously massive weaponry abounds in the Monster Hunter world, but at the small ends it's quite readily handled by completely stock GURPS rules; instead of large or knives as a sidearm, you carry a kukri/falchion/shortsword. Going sword and board? You have a broadsword or bastard sword instead of the shortsword that was the somewhat standard companion of shields for much of history. Spear and shield is still around and quite effective. The perk for Weapon Strength (counts only towards avoiding penalties due to low strength and benefits of high strength for things like one-handing a two-handed weapon, etc)
The first weapon shown is the old fashioned sword and board. Nothing of any difficulty or interest there, other than the possibility of making one from a giant monster's tooth or tail or whathaveyou.
Next up is among the most famous of the weapons from Monster Hunter, the so-called Greatsword. I'm inclined to have it use the 2hd Axe/Mace skill, and Very Unwieldy. High strength and it hits like a truck. You can also hold it in a defensive grip and use the Block skill with it and get a sizeable defense bonus. It is less a sword, than a bludgeon with a wedge for an edge. Telegraphic attacks are rather common to put enough momentum on it to actually swing.
After that is the warhammer. Larger than normal, but nothing really worth noting. The Maul and Great Club and so on serve well enough, bigger ones with more ridiculous strength requirements aren't hard to make.
Sword and Lance. The lance is basically just used as a spear, and in some instances IS just a spear. Other than possibly making an even larger Monster Hunting spear from the various ones listed (such as the boar spear, which is itself already a beefier spear). Not shown is a more aggressive version, called the Gunlance. I'll find a vid of that. A lot of them fold or telescope to save space when put away.
Next up is the Longsword, basically an odachi. To use it in GURPS, it's just a greatsword, or a slashing greatsword (+1 cut, -1 thrust), and maybe use the rules out of Dungeon Fantasy for making oversized weapons. Rules as written play in here just fine.
The Bowgun is, as far as I can tell, a TL5 or 6 pump shotgun, built at TL4(?). There's a lot of fairly intricate technical stuff that shows up in the series, but based on vehicles and stuff, it's probably a definite fantasy TL4, for TL4+1 or so at least. There's also a Heavy Bowgun, which is a larger, heavier bowgun. All of them shoot slugs by default, and you can load specialty ammo for elemental effects, things like bola shot, and buckshot. Big, fat, slow moving, heavy rounds? Sounds like a shotgun. Bows are also a thing, with ludicrous large knife to shortsword sized arrows that can be wielded in melee combat as such, but not shown in this vid. Ones in my world would come with a bayonet or striking area standard, because giant monsters trying to get up close.
Last up is the Switch Axe. A big two handed axe, the rear blade can fold up and over as the front of the axe blade slides down to turn it into somewhere between a greatsword and a longsword. All methods of achieving this are fairly complex, but reasonably doable. GURPS terms, probably a couple ready maneuvers to switch between forms, possibly with a chance of jamming (fast draw roll to switch faster?) Another weapon that works similar but in reverse is the Charge Blade, which is a sword and shield, but the shield can attach to the sword to make ludicrous axe. discussed later.
Now, on to stuff that didn't get shown.
The Gunlance. Essentially a bangstick with a bayonet. The chamber is loaded with rounds like the fancy, super-flash ones Hollywood uses to make ridiculous muzzle flash, for the purpose of blowing things apart. I see no reason you couldn't have a gunlance just have a proper shotgun in it, same as the bowgun, and it's just harder to use by virtue of being made for one-handed use.
Other than a few oddities like the spread-shot, the bow doesn't do anything you wouldn't expect. other than be ENORMOUS. Behold.
I'm thinking just a longbow, or compound longbow, with those heavy arrows trading range for damage over regular broadheads. Also, you can use them to stab and slash, because it's large by the standards of spears, let alone arrows.
The charge blade is a large shield with a mating sword. Used separately, it's sword and board as standard. Attach the shield to the sword, and it's a huge greataxe. More practical than the switch axe in that it actually comes with some defense when not in ludicrous axe mode.
Another weapon is the Hunting Horn. Basically a giant instrument that can be used as a bludgeon, it's just a musical hammer. I'd treat it as a means for magic-based music, or have one that similarly had syntactic magic runes built into it to be adjusted and used by the wielder, per Thaumatology.
There's also the insect glaive, but it's basically just another spear/polearm with a handy dandy helperbug. I'd probably not bother to make it its own thing, and just have the lances/spears usable without a shield.