Okay, so i read if you have fn nights, you have like a %50 chance of getting a dlore, whereas mw is like %10
Quality isn't what gives you a percentage. Its how many of them are in the trade.
If you put say, 9/10 different collection weapons in a tradeup, and one with the one you want, you'll have a 1/10 chance of that collection.
imagine if u have 5 cobblestone weapons, and 5 nuke collection weapons in one tradeup, your chance will be 50/50
edit:
that said, quality of weapon does determine the chance of a higher quality output.
so a BS would rarely or never get you a FN