Weapons could definitely use some balancing. I'm all for that.
For one thing, we could do with some more variety:
There are six different basic types of sword used in the middle ages: The thrusting shortsword/gladius, the rapier and other thin fencing swords, the chopping cutlass/macheti/broadsword/yataghan (and weapons like the falx, which despite being a "slashing weapon" had limited armour-rending qualities), the slashing saber/tulwar/shamshir/scimitar, the double-edged viking sword/longsword, and the two-handed greatsword/flamberg/zweihander (and hand-and-half bastard sword, which could be used either as a longsword or a greatsword, and which developed into the estoc.). Each performs differently, and is used in a different manner, in combat.
For axes, there is the hatchet/handaxe/francesca, the bearded axe/battleaxe/labrys, the two-handed long axe/lochaber axe/bardiche/sparth, and the two-handed, double-bitted bipennis (basically, a weaponized version of the common woodaxe)/doloire ("wagoner's axe", which consisted of a large, triangular blade backed with a hammer, and attached to a 5 foot shaft). Again, all four perform differently, and are used differently in combat.
Hammers come in the basic bashing variety, the beaked "warhammer" variety (a hammer with some minor features of a pick, mainly for armour-piercing), and the two-handed maul.
Maces really only have three different forms, the smooth bashing warmace/calvalry mace, the spiked or bladed mace/morningstar/holy water sprinkler, and the rare two-handed great mace/plançon a picot.
Spears can be short and one-handed (and occasionally heavy and clublike, like the godendag), two-handed, or of pike length. They can also be partisaned, up to the point of being practical tridents. Tridents themselves can be one-handed or two-handed, and spears can be bladed, as well as pointed.
Flails are another common medieval weapon. They're almost unique in having movable parts, consisting of a chain, or one to several linking sections, connecting a handle to heavy wooden or metal strikers. Flails can range in size and power from the scourge/cat-o-nine-tails (basically a more viciously weaponized version of a whip), to the classic ball-and-chain, up to a two-handed variety, which may have up to three heavy spiked balls.
Knives and daggers are another very common weapon. They range in size from tiny work-knives, that would have been carried ubiquitously, up to "knives" that only differ from shortswords, or cutlasses, in the manner in which they are used. Knives could be used for slashing, chopping, and stabbing, with the latter preferred by the nobility, in the form of daggers/roundels/poignards. Knives were also commonly used along with swords, in somewhat the same way as a buckler--namely, mostly defensively, to catch the opponent's weapon, and to block blows, while still allowing the occasional vicious stab. The long thin poignard could be quite effective against plate, being used to stab through gaps in the armour or visor, once your opponent was rendered prone. Such daggers were often very expensive, because of the demand for quality of the blade, as well as the prestige associated with them.
Picks could be weaponized, and weapons like the bec de corbin/crowbill (one handed) and lucern hammer (two handed) were, basically, this.
Polearms came in a bewildering variety, but other than the weapons already mentioned, probably the most important were the halberd (not very dissimilar from a lochaber axe, but the addition of a long piercing spike, and a picklike beak, gave the wielder more options), the corseque/ranseur (similar to the trident, but with bladed tines), the sword-staff/rhomphaia/war scythe (a sword, scythe, or falx blade on a long pole), the military fork (basically a "trident" that was as often as not a pitchfork head on a reinforced shaft), and the billhook (a heavy chopping blade that curved back into a pronounced "hook", on a reinforced shaft).
Aside from these melee weapons (and obviously, some of these could be thrown, and there are versions of these weapons I didn't list, like the harpoon, pilum, or bolas, that are intended for throwing), bows, slings, and crossbows also came in a variety of forms.