Couple of things.
The Alien Influence already exists in the system. This is done in extraordinary items via the “Damage” property.
Generally flat modifiers are steered away from in OL except in the cases where Multi-targeting could be effected (hence why knockdown is a flat modifier instead of (dis)advantage in the case multi-targeting some who are knockdown and some who are standing).
The concept of damaged weapons is interesting, and you could do this by simple disadvantage. Remember that “damage” is not actually hitting someone, but chipping away at their ability to remain in the fight itself.
Attribute rolls (with or without weapons/items) are how well you use what you have, how effective you are with the weapon itself, not how powerful the weapon is necessarily. So I see what you are trying to do with it effecting damage after the roll, but it certainly is very counter to what OL is about, especially with Success with a Twist mechanics.
For making interesting loot, I’d recommend @SamWilby GM Tech Article here:
Overall would it break things… probably not? But if your issue is fun/interesting items/loot for your players, there are other ways to go about creating that. I like to lean more on expendable and consumable items myself.