Here are a few extra weapon options - they are certainly not in Tolkien's works but they are weapons that would fit into the same 'historical' timeframe. They maintain a mechanical balance that makes them distinct from other already existing weapons.
Staff Sling 4 14 2 Brawling Ranged Weapon
Notes: This weapon breaks the rules a little - it has 2 upgrades over the sling rather than 1, this is because it has to be mechanically better than a Bow otherwise no one would take the -1d hit to accuracy because it belongs to the brawling category. Still a dubious choice to take a -1d to hit for +1 damage and +2 Injury. Mainly here for completion.
Bill 5 14 3 Spear 2-handed
Falchion 3 18 2 Swords -
Composite Bow 4 14 3 Bows Ranged Weapon
Notes: These three weapons are intended to be what the Mattock is to the Long-hafted axe in the Axe group. They have a mechanical trade off that makes it a distinct choice to the Spear/Sword/Long Bow respectively. As with the Mattock, they would be rarer weapons and may only be used by distinct cultures.
The Bill is a halfway weapon between an axe and spear, It is more damaging than a spear but does not Injury as well as a spear used two handed (this is for mechanical balance) It also loses the ability to be thrown (for obvious reasons) and keep the same Load.
The Falchion is a alternative to a normal Sword. It loses 1 damage but gains a +2 Injury while remaining the same Load.
The Composite Bow is an alternative to the Long Bow I came up with. It switches a +1 damage rather than +2 injury over a normal Bow for a +1 Load (this is for mechanical balance reasons).
So there you are, distinct mechanically different weapons that add more choice for players. It may be the case that I have overlooked some other hidden mechanical balance factor that makes one of these better than intended - please feel free to point them out if you see them.