I don't think it would be too hard to remember what weapons are, since it's not going to change over the course of the game. If I can name 150 pokemon, I can remember that a Zongonash is a kind of spear and a Gonhotir is a kind of hammer. There's allegedly only 7 weapons to keep track of in your own civ, and having to look up what a foreign weapon is will make it that much more foreign. I for one play DF with the wiki open at all times, so the need to look up a term causes me no shame.
It might help to give weapon names in both English and Dwarven as we do with surnames(although I'm not sure where you would put that). A Cut-Lass is probably easier to remember than a Rit-Saruth. A lot of weapons have quasi-meaningful names, for example the cut-lass sword and wind-lass crossbow, tri-dent mean three-teeth, hal-berd means staff-axe, a bec-de-corbin is a crow's beak, a morning star refers to its shape, a Lucerne hammer refers to the city that invented it. There are also weapons related to their home civs, for example the Saxons used a kind of dagger/sword known as a sax or seax, and the Franks were known for their francisca throwing axes. Rather than just throwing attractive syllables together, the random name generator could combine meaningful words. For example, Danman-libash is heavy-axe, or something more poetic like Vumshar-obok, gloom-pillar.
Getting the machine to come up with "logical" weapons names would be an interesting task. Using the previous examples, you would program it to relate danman/heavy with weapons that have a higher size than the default, and libash/axe would be related to weapons that are based on the axe. Obok/pillar could be related to shaft weapons, like spears or staffs, and vumshar/gloom could be a generic word that goes with any weapon. So the machine would modify the weapon and then use its properties to eliminate certain words from the list and then pick a randomized name based on the remaining result.