Not trying to necropost here, but If i recall correctly, at least on the privateer remakes,(Privateer Gemini Gold, Privateer: Parallell Universe, and others...) which uses the source code from the ORIGINAL privateer (which this game is) then difficulty is not tied to upgrades.

it is actually tied to how much money you currently have.
but hey, for all i know they could have changed it somehow. All i know is that when i play the remakes with the upgraded graphics, I always keep my hex editor open, so that if things get too difficult, i just take some of my money away (keep a note of it, so you can add it back in port. cheat if you want with this method, but it takes the fun out of it. I just pretend I'm stashing my money in a mason jar and burying it on some backwater planet...but thats me... you can just pretend you are banking, lol.)
Again, this is from the source code projects, but from what I recall, they used the code the same way that it was for the original. The main thing they modified was the graphical capabilities so that you could run it in HD at super high resolutions.
anyway, just something to think about. (and maybe try, for those of you getting hammered when you get a better ship.)

Ah, so it's based on your finances? Interesting. That would make sense since this game encourages stockpiling huge amounts for the next ship or whatever.

I don't think it's correlated to finances.

I thought it was based on kills and missions completed. I'll give it a shot with the weapons/shield theory

That may due to the fact that stuff you buy for your ship is still considered part of your total 'assets'. The value of the assets figured into the total credits. The same way the game knows your total ship "assets" whenever you about trading in your ship for another, and gives you back certain mount if the value in your previous ship (with upgrades) is greater than the value of the new ship (without upgrades).