Alright what is going on here?
Since you are a human and work for the Alliance, and since humans are war profiteers by nature, most of the guns in the game are human.
Claymore is human. That's the end of the discussion. It was a human design, even if it was too powerful for humans. Is a for profit company going to flush their R&D money? Nope, find a new market.
Widow is of unknown origin. Whether or not it appears in the Geth Server mission is irrelevant, since all the Quarian soldiers carry Vindicators and wear their environ suits. Legion states that images in the consensus draw from Shepard's memories, and are just a representation of the historical facts. However, even if this wasn't the case this remains ambiguous since the Quarians didn't invent the Geth until they were already minor members of Council space. So it is possible that the weapon was bought from a different council race. Vindicator is ERCS and Turian, and perhaps it existed back then.
Weighing in at 39 kilograms, the Widow Anti-Material Rifle is primarily used by sniper teams in assault missions against armored vehicles or krogan. While kinetic barriers offer effective protection on vehicles, the kind generated by conventional military field generators are far too weak against the Widow.
The Widow was never designed to be carried and fired by a human. Although this modified model can be carried, no ordinary human could fire it without shattering an arm.
Perhaps it was really Quarian, but it is really just unknown. One of the races likely invented it for the role in the description. Perhaps it is really Asari?
Legion has a "Geth Rifle," but the Geth just gave Shepard specs for a rifle that could be fabricated in SR2's armory most likely, so it was probably a modified organic design of some sort.
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Carnifex isn't necessarily human, the best evidence is just that you can buy it from Kassa, but other guns can be bought from there as well that are likely not human. Phalanx is definitely human, or at least developed for humans. Predator is ERCS (Turian).
Mattock is a human weapon, and the Argus was intended to be a development of the Mattock. Revenant is unknown. In ME2 even Geth run them.
Eviscerator is human, and Wraith might be human (although could have been modded by someone else).
Scimitar and Katana in game are supposed to be from Ariake, and as such they are human. Scimitar in ME1 was Elkoss and therfore volus.
Shuriken is Elkoss and volus. Tempest is ERCS and therefore Turian, like the Vindicator. Locust is Kassa and human.
Mantis is Devlon, but I am not sure what race owns that company. Viper is Rosenkov (human). Don't know about Incisor, it is bought from Kassa but is otherwise indeterminate.
It is tricky to do any of this though because as we see in modern times a weapon could be designed in one country, but manufactured by a different country's firm. Is an M16 made by FN American or Belgian? Avenger is an Elkoss produced weapon, but standard issue in the Alliance. I would call it volus for this purpose though (don't know who submitted the design).