What weapon stats matter for squadmates?

Weight: Is irrelevant and can be ignored.

Capacity: While companions have unlimited ammo, they are restricted by the clip size of a given weapon - it affects how often they reload, and, by extension, their overall rate of fire as well as time spent in cover.

Fire Rate: Obviously companions are affected by this. Rate of fire is just as important to their damage output as it is to Shepards.

Damage: Again, this is just as important to companions as it is to Shepard.

Accuracy: Accuracy does matter for companions. Even though it can be assumed that the AI isn't going to fire wide on purpose, accuracy has a noticeable impact on, for instance, the spread of pellets from a shotgun blast, or the level of 'drift' during a sustained burst with an SMG or Assault Rifle.