So I've done a little bit of testing on this and have had similar effects in mulitple run throughs. I can't say I'm 100% certain on what is causing this, but I believe its the second Mod you can get from a Control room with prismium if you start your run with the Billhooks. It seems to make its damage and the damage of any cloak weapon grow expenentially as you progress from floor to floor. It was hard to notice this when I wasn't upgrading the Billhooks second mod until later in the game but for my most recent play through I decided to go gung ho and make sure I could immediately upgrade my Billhooks with both mods the first time I got to a Control room. The damage increase was very noticable when I did this by the end of my run.
I snagged a few screen shots of my run through to show you what I am talking about. For this run I decided to go with common cloak weapons. One of my screen shots is at room 5 of the Modern Warfare Department well after I had the second Billhooks Mod. The following one with larger damage is when I had made it to Natural Disaster Floor 2 and found a cloak weapon that also had really high attack power. The other 3 screen shots are all how my weapons were sitting before I fought Ms. Imamura at the end of my run and I was able to take her out with two shots from my bow. I appreciate the easy runs though, but thought you guys may want to know about this!