There's no documentation I found anywhere aside from people not liking it or a few tests where it seems to perform well. The wikis just say it does +X damage. Well, I noticed that "X" is different on different weapons and non-existent on some.
My theory is this:
Each Dmg mod adds 2% to the base DPS of a ship weapon.
There are several important caveats here: That is NOT DAMAGE per strike or "Damage per Volt" (DPV). Also note that mark and rarity affect base damage.
So weapons that do not have a stored DPS rating (like mines and torpedos) receive no benefit. They have damage but it isn't per second.
Also, I believe a purple Mk XII weapon has higher base DPS than a blue Mk XII weapon or a purple Mk XI. More base DPS means a higher benefit from Dmg.
See... My theory is that Dmg may be the BEST PvE modifier on Dual Heavy Cannons, followed by Dual Cannons, followed by Single Cannons, followed by Dual Beams.
It would be awful for turrets and most beams and useless for mines and torpedos.
Part of the idea here may be my suspicion that instead of multiplying damage by rate of fire to achieve DPS in STO, STO starts with DPS and filters through cooldown to determine damage per strike on all non-mine and torpedo weapons.
So fast weapons do better and higher damage weapons do better and weapons that are both fast and high damage derive exponentially more benefit from a Dmg mod.
I think maybe this has gone mostly unnoticed because people aren't fully distinguishing the value of different mods to different weapons and because I can't find a theory of what Dmg is even supposed to do so people have been acting like its value is constant across weapon type.
This is somewhat understandable because a Blue Mk XII beam or cannon gets the same benefit from CritH over time and a Blue Mk XII CritHx2 weapon gets the same crit boost as a Purple CritHx2 Acc weapon, assuming no accuracy bleedover.
However, I'm suggesting that Dmg is highly multiplicative and, further, that cannons get more boost than beams over time and that a Purple Mk XII Dmgx2 Acc weapon gets a bigger damage boost from the Dmg modifier than a Blue Mk XII Dmgx2 weapon.
That suggests there is a threshold where Dmg scales better than other mods and it will probably be noticeable in cannons first.
There was one person not long ago who got better results from Fleet weapons than with Borg. I suspect that was using cannons. I also suspect he'd get better results if he swapped out his turrets for Accx3 or Borg turrets (instead of the all fleet/all Borg/all Acc test) but used fleet cannons in the front.