I swear it wasn't doing this when I started the game, but sometime in I think Solitary, I started to notice this weird sound playing whenever I used a weapon.

https://youtu.be/NRXcG9QfFm0

I even started a new game and oddly enough, the sound wasn't there. Everything played normally.

I actually just came here to ask about the same thing.

I figured it out a few days after I posted this. It's not a glitch; weapons actually will always make that sound when you increase your "Power" stat, hence why you won't hear it on a New Game. It eventually gets to the point that the weapon sounds are drowned out completely. :/

Well... that's a strange design decision :P