Who were the weapons-makers for the Norse gods? Was there a specific god like in Greek mythology?
Dwarfs, mostly. Some particular examples:
Gungnir: created by the Sons of Ivaldi (Prose Edda, p 145)
Loki went to those dwarves who are called Ívaldi's Sons; and they made the hair, and Skídbladnir also, and the spear which became Odin's possession [Gungnir]
Mjölnir: created by Eitri and Brokkr (Prose Edda, p 146)
Then he [Eitri] took from the forge a hammer [Mjölnir], put all the precious works into the hands of Brokkr his brother...
Dainsleif (Prose Edda, p. 189)
Thou hast made this offer over-late, if thou wouldst make peace: for now I have drawn Dáinsleif, which the dwarves made
Tyrfing: created by Dvalinn and Durin (Hervarar Saga (1. KAPÍTULI))
And just maybe Völundr (Wayland the Smith) (who forged Gram), who might also have forged:
Norse gods didn't have a "smith" god (like the Greek god Hephaestus or his Roman counterpart Vulcan). In spite of being polytheists they didn't divide every aspect of their lives in the way that other cultures (Greek, Roman) did.
In Norse mythology most of the "cool crafts" where done by the Dwarfs (Dwarves).
[Dwarfs had] a far greater cleverness in the arts and crafts of working with iron and gold and precious stones. These Dwarfs, with Durin as their king, made rings and swords and priceless treasures, and mined gold out of the earth for the AEsir's use
(Roger Lancely Green. Myths of the Norsemen)
There are though "legendary" smith figures in the Norse mythology beside the Dwarfs, like Waylan the Smith. Wayland (sometimes Weyland or Weiland) is, according to Völundarkviða (a poem in the Poetic Edda), one of the three sons of the king of the Finns. But, in spite of being a legendary master blacksmith, he didn't forge any remarkable artifacts nor any of the god's weapons. He is also a human figure (although maybe with skills that could rival with those of the Dwarves) not a god.