So Weta Workshop did a lot of work constructing the many named weapons mentioned in Tolkien's lengendarium. What's more, in the Simarillion and Unfinished tales there are plenty more described in detail. Do the designs have any parallels that exist historically?
We have Elvish blades which were usually curved, inlaid with runes and writing with thin profiles. While they look very elegant I'm not sure that they would be useful in battle barring their supposedly excellent material properties. Examples are Sting, Orchrist, the Lhang and the more western looking Glamdring (Which was apparently used in conjunction with Orchrist). There are also a few other weapons mentioned or used by Elves sharing similar aesthetic properties like Aeglos the spear.
We have the weapons of Men and good examples of them would be Herugrim, Guthwine, Andurill and Narsil.
Orcish weapons are crude but they have their very iconic scimitar as well as Morgul blades.
Dwarves use very heavy and thick double headed axes, warhammers and angular shortshorts and knives.
So are these purely works of fantasy on the propmakers part or do they have some basis in functional military weaponry?
Some yes, some no, at least not that I am aware of. The designers used in the Lord of the Rings films used historic weapons as a guideline, but they also developed highly stylized weapons for particular characters that were more about visual impact than historical tie in. That works pretty well with the Tolkien concepts, his writing is a presentation of a new form of legend based on ancient NW European mythology, and it has a mix of the historic and fantastic in it at all stages. To look at the weapons you mention specifically I will let you know which have a historic precedent and which to my knowledge are made up. Someone may be able to correct some of these so at least for the ones I can't identify do not consider my comments a final word, there are so many forms of weapons from so many cultures, some highly stylized themselves that I wouldn't be surprised if someone recognizes at least one I haven't seen.
Weapons of Elves:
Sting: A highly stylized variant on a medieval dagger. Most medeival dagger's are much slimmer and less curvaceous than this though.
Orchrist: Looks made up for the movie to me
Lhang: I haven't seen anything quite like this before.
Glamdring: Looks very much like a typical crusaders two handed two edged sword, very common medieval design. A good modern (but historically important) analog would be the Sword of Stalingrad, made by Wilkinson's in England for presentation by King George V to the people (and government) of Russia in honor of the great sacrifices of Stalingrad: http://orientalreview.org/wp-content/uploads/2013/02/Sword_of_Stalingrad.jpg Here is a link to a Mamluk Sword of similar style: http://sword-site.com/thread/218/oakeshott-sword-mamluke-arsenal-alexandria?page=1&scrollTo=566
Aeglos the Spear: Looks like the Lhang
Weapons of Men:
Herugrim/Guthwine: These appear to be the same or similar, and look like a fairly close copy of the Roman Gladius. http://www.romancoins.info/milit-gladii-Nim.jpg
Anduril and Narsil: Like Glamdring a design common to the medeival era, similar to a crusader's sword or a Scottish claymore.
Orcish Weapons:
Scimitar: Looks like it was made for the movie to me.
Morgul Blades: Variant of a typical medieval sword.
Dwarves Weapons:
Double Headed Axe: A bit too stylized for a real weapon, likely
War Hammer: Looks very similar to many historic war axes (real battle axes were much smaller than most childrens imagination of such a thing). The main difference is the head extends to both sides of the shaft, most war axes I have seen have the entire head on one side of the shaft and no counterbalance: http://www.cullodenantiques.com/images/european_horsemans_battle_axe1.jpg
Knives: looks like something made up for the movie to me
Sting is based on the Xiphos, a Greek Iron Age sword: http://www.ironagearmoury.com/xiphos7.jpg
Orchrist is based on a Falchion or Messer, European High Middle Ages swords: http://www.myarmoury.com/images/reviews/mrl_falc_e_s.jpg
Lhang I don't know.
Glamdring is similar to a High Middle Ages European longsword, with a more Xiphos-like blade: http://www.coldsteel-uk.com/store/italian-sword-88its-full-1.jpg
Aeglos - closest would be a Naginata, a Japanese sword-on-a-stick pole weapon from the Kamakura period: http://upload.wikimedia.org/wikipedia/commons/c/c2/Naginata.jpg
Herugrim is like a Gladius: http://upload.wikimedia.org/wikipedia/commons/7/71/Uncrossed_gladius.jpg
Guthwine is like a Viking sword: http://www.weapons-universe.com/Brands/Valiant_Armoury/Viking-Sword.png
Anduril is a longsword, which I already linked.
The Orcish scimitar is like a falchion variant. Why you would want a weapon without a point when you could just as easily make it with a point is beyond me, but it's been done (albeit rarely): http://www.wulflund.com/img/goods/en/medium/falchion-maciejowski-bible-13th-century_2.jpg
The Morgul-blade is based on the nearly infinite variety of knives and daggers that have existed. I question the usefulness of a hilt that rounds back.
The Dwarvish axe is nothing like a real battle axe. Something like the Dwarvish axe would be useless in battle - too heavy, and no benefit from the second head. Polearms and weapons with complex heads existed, but they always had a variety of different types of weapons up there, to provide tactical options. A real battleaxe looks like this: http://www.darkknightarmoury.com/images/Category/medium/16.png
The dwarven warhammers are similarly absurdly designed. Compare the size of the head on a real warhammer: http://www.medievalwarfare.info/pics/warhammer.jpg
The dwarvish knife also looks like a dumb design to me, but knives have been made in a staggering variety of forms, and I am not an expert on them.
I'd be more than happy to elaborate on any of these that interest you!
The guys that designed the weapons for the LOTR used quite a lot of inspiration from real-world weapons, and at the same time wanted to give them the feeling that they belong to a certain culture. Gondorian and human weapons were based on different European weapons and armour, Rohanian were horse vikings with a dash of leather armour, because there is no real fantasy without leather. Elvish.. well I have no effin idea, but they do have a very japanese feel to them. The dwarven weapons follow a more or less viking appearance.
Now the Hobbit... well I'm not sure if the props in the Hobbit were done by WETA, but they are much worse than the ones in LOTR, and follow the standard fantasy cliche's you see in WoW for example. This is one part of the hobbit movies that I really hated.
That said, the Sting is based on either a Xiphos, or on celtic-age leaf-blades. You'll see pictures in the thread. I remember reading an interview about Glamdring being a mix between a long-sword and a celtic leaf-blade sword
I'd argue that Orcrist and the various big ugly orc weapons were based on falchions and messers. I think herugrim is definitely not based on a gladius, but rather on viking swords which also fits the "norse on horse" view that Rohanians follow.
The weapons of the nazgul are pretty standard longswords and daggers.
The weapons and armour of Gondor look like a mix between XV-th and XVI-th century european armour, pavise shields and a bunch of weapons like normal swords and spears..
