[Update: I'm pasting Scott Kleinman's comment up to the end of this entry because it significantly expands and improves my discussion.]
Some interesting discussion at Unlocked-Wordhoard and Gypsy Scholar. In fact, the discussion is on far more substantive issues than this one word, and I hope to be able to discuss the actual content soon, but for now I'll have to be satisfied with being a philologist pedant.
The context of 'weapontake' in Tolkien is the "Muster of Rohan," when all the men able to bear weapons are assembled in preparation for the ride to Minas Tirith. It seems from the passage (RK, V, ii, 72) that Tolkien is using the word to mean the assembly of all the able-bodied men of Rohan in companies. Although a folk etymology might construe the passage as meaning that the king provided the weapons--i.e., the able-bodied men arrive and are issued weapons from the king's armory-- (as was the case in Peter Jackson's depiction of the Rohirrim in both The Two Towers and The Return of the King), I don't think Tolkien intended that meaning, and I don't think that would be accurate for Anglo-Saxon England (I could be wrong here).
"Wæpen-getæc" is an interesting word, and I wonder if Tolkien might not have worked on the definition of "weapontake" for the OED: he wrote the definitions of a number of words beginning with "w", including "walrus."
The etymon for the word seems to be ON "vápna-tak," though this is used in a different sense. It is, according to Bosworth-Toller, a Northern word; in the south "hundred" was used (which is why I think that folk-etymologizing the word and assuming that it means that men showed up somewhere to "take" their weapons is probably wrong), and its being Northern would explain the ON etymon. Bosworth-Toller gives the primary source as the laws of Edward the Confessor.
The point here is that Tolkien is likening the Rohirrim to the Anglo-Saxons yet again (even though the "Northern" word is a bit of a curve ball here, since the Rohirrim are linguistically Mercian), suggesting that at the king's call, all the men of Rohan were expected to assemble for military service and form themselves into companies that were, apparently, led by the professional soldiers of the king's household. This practice is in contra-distinction to the customs of Gondor, where a large, standing, professional army was in place.
The larger point is that Tolkien is not merely being archaic for the sake of archaism: he is being particularly precise, using exactly the right word (both in terms of definition and cultural connotations) that he needs for this particular situation. Tolkien's sense of the "right" word, which includes sound and etymology, is actually more 'theorized' than the word choices of the great Modernists to who he is often unfavorably compared (do you really think Faulkner, or Hemingway, or Woolf knew anything of the History of English; they were great talents, but they were working by gut instinct. Joyce is a somewhat different case, but he was no historical philologist--although knowing and sampling so many languages made him more sensitive to the interconnections of European languages). .
[Here's the comment from Scott Kleinman.]
Here are some thoughts on weapontake. The Old Norse use of vápnatak seems to have involved the confirmation of a vote at an assembly. In England, the word came to be used for the assembly itself and was, in areas with heavy Danish populations applied to the local judicial body. It was probably also used for the place where the assembly met. As the administrative and judicial boundaries within English counties became more stable, the sense was extended to refer to areas of jurisdiction in addition to the bodies themselves, rather than just the body or the place of the court. We can thus see a sort of evolution in the word from the taking up of weapons to an area of jurisdiction, and it might be possible to locate Tolkien’s usage on this timeline.
It seems to me that, when Tolkien writes that ‘all who could be spared were riding to the weapontake at Edoras’, he could mean a point of assembly, but probably not an official jurisdictional unit for the region of Edoras (the precise meaning of which is also quite interesting, especially given its use in two different senses in Beowulf 1035-1045). In other words, it’s in the middle of the timeline. But, of course, there is no necessity to assume that the weapontake of the Rohirrim accurately reflects the wapentake of Anglo-Saxon England, since the Rohirrim do not exactly match the Anglo-Saxons. Tolkien modernises the spelling (unlike Edoras), which, conceivably takes it in a new—or an alternative—direction consistent with a possible folk etymology: a taking up of weapons as part of a military gathering. The modernisation of the spelling curiously gives the word a more archaic effect by restoring the original connection to weapons. Perhaps this was necessary. Words like Edoras don’t seem particularly archaic to anyone who doesn’t know Old English; they’re simply foreign words like Minas Tirith. But if Tolkien wanted to give the sense of something familiarly English, but archaic, the term weapontake worked pretty well.
As a side note, Higden’s definition is very interesting. Here it is in John of Trevisa’s 1387 translation (with the thorns changed to ‘th’ and yogh to ‘y’): ‘Wepentake and an hondred is al oon, for the contray of an hondred townes were i-woned to yilde vppe wepene in the comynge of the lord.’ I take this to mean: ‘A wapentake is the same as a hundred, for the country of a hundred towns were wont to present weapons at the coming of the lord’. Clearly the word was prone to folk etymology, and it is not impossible that Tolkien had something similar in mind; i.e. Théoden would take the weapons offered by the those who owed fealty to him.