Again, I'm re-reading the Lord of the Rings trilogy and am still on book one, so my question is going to refer to the movies.
During the time The Lord of the Rings stories take place, Middle-earth is not bereft of magic (for lack of a better term) or the supernatural. The One Ring exudes tremendous power; the spirit of Sauron survived despite his physical destruction.
Gandalf and Saruman both have staves that can perform magic and presumably both Gandalf and Saruman are very powerful wizards (in fact we see Gandalf get angry with Bilbo at the beginning of The Fellowship of the Ring, saying "I am no conjurer of cheap tricks.").
The elves provide magical items to the fellowship (rope; knives; lembas bread; the Light of Galadriel; the Mirror of Galadriel; the Elven cloaks). As well, it is Galadriel's ring, Nenya, that protects Lothlórien from evil attempting to enter. The elves also show the ability to provide advanced medical treatment. There are the palantíri, which could show visions or intended thoughts of the users (Palantíri at the LoTR Wikia). Arwen summons a flood of water in the shape of galloping horses to defeat the Nazgûl at Rivendell. These are just some examples.
Why then are the weapons used in the War of the Ring so rudimentary if magic and "spiritual" powers exist in Middle-earth? Swords, hand-held shields (some wooden, even), knives, axes, bow and arrow, spears, and morning stars/flails are used in the war(s). Why could magic not be channeled in some way to give those fighting against Sauron a greater advantage? Why just the basic weaponry?