Ironically, aside from Arbiter and Osiris, it was the game's two least important weapons, Revenant and Kablooey, ones which had an actually deductible origin. One can infer that Revenant was either invented by The Order has a weapon against demons or discovered like them. Meanwhile, all we need to know about Kablooey is told by Vergil: it's a powerful demon weapon disguised as a normal taser gun in the human world.
However, Aquila and Eryx, which become two of the most used weapons in the whole game, just pop up out of nowhere, Aquila being the wors offender. Eryx appears when you kill Succubus, a demon, it's a demonic weapon. Maybe you absorbed some power in her or something. Then you kill Bob, another demon, and get...an angelic weapon. And that's when you realize that Eryx's appearance was just as out of nowhere as Aquila's just then.