Expanding a little bit on my "pointed swords relatively poor at thrusting should just do less impaling damage" idea buried in the comments on Thursday, here are some ways to make weapons functionally different. As in, ways to let them reflect relatively small changes in weapon design that can have a material difference on how they fight in battle.
Pretty much there are a few ways you can differentiate muscle-powered melee weapons on the actual tables - among them damage, damage type, reach, ST, cost, weight, parry. Buried in the weapon descriptions, though, there are more. All of these examples come from GURPS Low-Tech. This isn't exhaustive, or in order.
Throwability: Can you throw it effectively? That's such a big change it changes the name of at least one weapon (the Throwing Axe.)
Chinks in Armor: Some weapons target weak points well. The estoc and stilleto ignore -2 of the penalty to attack such weak points.
Fragility: Weapons made of fragile materials, such as the tebutje or macauhuitl, which wear out quickly against DR 2+.
Inflicts Defensive Penalty: The shotel is -1 to Parry or Block because its curved tip lets it stab around shields and parrying weapons. The entire category of flails does this too, to a lesser or greater extent.
Gets Stuck: Picks, barbed weapons, and most swing/impaling weapons have this feature. They go in, and do extra damage on the way out.
Hard to Disarm: Rondel daggers get this one - they're designed to pair up with locking gauntlets so you can't drop them or have them disarmed easily, so they resist disarms.
Armor: Some weapons have built-in armor, usually in the form of hand protection - the cutlass and pata have this.
Good at Disarms: Technically a table note, like Gets Stuck. But some weapons are especially good at disarms, and ignore the inherent penalty for using the move.
Remove Foe's Options: Partisans (and boar spears) have a crosspiece to let you ignore the optional rules for foes running up a spear (GURPS Martial Arts, p. 106).
Extra Attack Modes: For these, see LTC2. Some weapon variations have more ways to strike you due to hammer heads on the peens of picks and axes, axe heads on the backs of picks, spiked tips for stabbing, etc.
That's not an exhaustive list, but coupled with basic changes to the weapon, such as giving a sword bad at impaling lower basic damage (so it's functionally bad at impaling), or an excellent parrying weapons a Parry bonus, and so on, you have a lot of options to make weapon variations vary. And those matter a lot in combat, which is yet another thing I like about GURPS.