Well, the negative values is still a complete guess, and I'm not willing to bet on that - but consider this:
All upgrades do effect the weapon they are on
Upgrades that 'chain' together have additional bonuses
There is a base stat/base stat multiplier for certain stats on a weapon/tool
Additionally, there is this weird thing I am seeing with the badge and an icon like a fire, a number up upwards facing arrows and a +[num] val, which also seems ambiguous.
It's obvious there is a lot more going on with upgrades than literally just 'put an upgrade anywhere in a weapon slot and then it should just work' - but WHAT is happening is all just a guess from here. I would be surprised if 50% of my guesses were right.
edit: retrodigitial back on twitch