@STG_Mordin
I think there are certain weapon parameters that are local (mag size and rate of fire), at least in some cases. So I wouldn't worry that they are somehow modifying your game.
Given that, I think it is best to just accept the occasional cheat (as you mentioned you normally do). It's a 11 year old game, and co-op at that. So yeah, when it happens to me, I just last through that game and drop lobby (more annoying if it is yours, I admit).
I don't think that's how it works.
As an example, there's a mod on NexusMods which removes shotgun fire delay in multiplayer. The host must have this mod installed to have any effect. Clients without the mod installed on a modified host game will be unaffected.
So yes, if he can change parameters in my game without me having to install the same modifications then I am rightfully worried.
