I think grouping weapons by mission would be more "natural" solution than arbitrarily grouping them by tiers.
E.g.: you win a safe house. You'll get "safe house debriefing prereq" for this. Researching "safe house debriefing" would automatically research all weapons that can be in hands of cultists there. Barring some arbitrary exceptions, like cult-specific weapons (QBU, Wakizashi), that you'd research manually.
Doing this for apprehension, safe house and outpost for each cult (12x missions), I eyeball you'll be in ballpark of 50 weapons researched. This is not much, but honest work looks noticeable. Same could be done for farmers, initial apoc encounters and such.
Issue 1: As Solar said, I'm not sure OXCE allows to freely grant multiple researches for a single research. Except in interrogation manner, where you have to repeatedly research same topic, which defeats the purpose. Maybe it could be done if this research block that grants weapons is a single dependency for the weapons. Maybe you can tie weapon researches directly to completing the mission, but I think it's same issue you can be granted only one research for winning.
Issue 2: Interrogation pool for many captures contains common weapons. As such, it will be shortened now. I'm not sure how this affects the balance, probably not much.
Maybe OP would be interested in making a submod for this.