This was done a long time ago, so I'm just publishing the results here for anyone else to take this data to revise it or do what they wish with the information.
I don't remember what I did (sad, but true), but I found out a pretty accurate value of what the Weapon Allowance (WA) was, and this value can be found (closely) in Verifex's script to calculate your WA on the Train page. The exact value I calculated for WA to be was: WA = totalExperience * 1.69992. As you can tell, the number of significant digits was how close I was narrowing down the value.
Now, say you want to figure out how much PR a weapon will add with a certain NW. I did some data collecting. It appears that the formula to find out how much PR that will be added to your current PR, with a certain WA is: y = (0.4861)x0.8015, where y is the value of PR to be added after the weapon is equipped, and x is the value of the NW of your weapon minus the WA.
How do I use this and check its calculation?
First of all, unequip all your weapons, or unequip the ones that you don't want to calculate PR addition for. Write down your PR. Write down the NW of your weapon you want to add. Go to Verifex's script training page and write down your Weapon Allowance.
Now, do the calculation (Weapon of NW - Weapon Allowance). Plug this number as x in to the y = (0.4861)x0.8015 equation. This will roughly tell you how much PR you should add. So, if you want to know your estimated final PR, take this PR addition value and add it to your PR that you wrote down at the beginning without the weapon equipped. This should be roughly what your PR is when you equip the weapon. Confirm this number by actually equipping the weapon. How close was it?
Note: Numbers that contain high PR's and high NW's of weapons give better results, apparently. I was able to get within 2% of some estimates.