Grading system has been once again changed and completely redesigned since v2.1.0.122!

The grading system used to take into account weapon's Mods. This was very subjective and often did not match your own personal opinion as to how important the mods are to you.  Some people never cared for MeleeD bonuses, some people only cared for Attack bonuses, some people (archers) often cared for MeleeD bonuses more than others, etc.  Since version 2.1.0.122 I have decided to take the Bonuses(Mods) out of the equations and concentrate purely on the potential damage that the weapon can do when fully tinked and imbued.  The grading is completely and totally objective now.  BS/2 now reports Damage Grades and not Uberness Grades.

What it is:  Weapon grading system is a set of formulas that BS/2 uses that rates how good your weapon COULD BE if pushed to the max with imbue and tinkers.  This is critical to understand in order to save yourself from a lot of questions later.  It assumes that you will be successful in landing an imbue and a "safe" number of tinkers on the weapon.  Thus it will assign same grade to two weapons with the same starting stats... even if one of the weapons has been say imbued and tinkered some with iron/granite.

Who is it for: for people who are looking to be more aware of the loot they find.  There are very important stats that are often not understood on a weapon and are discounted as non-important.. or perhaps counted as too important when they shouldn't be.  This system is to help us all put everything in perspective.

How does it work: it uses a set of complicated formulas to equate weapon's maximum damage, variance, and craft into one number.  Just like when you auction goods on Vault, you want to have a common point system so that people who are bidding know who is ahead.  Same thing here: grading system that assigns "point" values to maximum damage, variance, craft calculates how far can your weapon be pushed with extra tinkers and comes up with a total "grade".
To be more precise, it comes up with two grades.  Every weapon usually has a wield requirement.  Often a weapon may not look "uber" for a 325-wield weapon but may be uber nevertheless in a lower wield requirement category.  For this reason, BS/2 will report you two grades: 1st - grade of how well your weapon stacks up against best weapons with the same wield requirement, 2nd - grade of how well it stacks up with the best weapons with the maximum wield requirement (325 for melee weapons, 290 for missile)

What are the gotchas: You should never ever use ONLY damage rating to determine the price of a weapon.  You must always always look to see if an item has any tinkers and imbues.  Remember: the grade does not care for how many imbues or tinkers you weapon has.  It only cares how far your weapon can be pushed.
Another important thing to remember: I will try to do everything I can to keep the formulas stable, never changing, so that you all have a reasonably stable measurement stick to measure your weapons against.  However, always remember that formulas are subject to change -- especially if I find bugs in them, or if perhaps Turbine changes loot mechanics again.
Due to how the formulas are calculated and how your weapon will behave, DmgGrades will change as you imbue your weapon with a non-AR like imbue (i.e. CS or CB)
 

What are the formulas:

New in 2.1.122

Each weapon is measured against the perfect weapon in the following matter:
First step: Formulas take the weapon and pretend to apply iron/granite and imbue to the weapon in the most proper proportions. For example, BS/2 finds an 18-36 Craft 10 sword.  It assumes that it is safe to do 5 more tinks to it. One is used up on an Imbue, another 4 on Granite and Iron.  Because the best results will be achieved by applying all Granite, that's what BS/2 does and comes up with a 28.63-36 sword with an AR-like imbue.

Second step: With the resulting weapon, the formulas calculate "Average Damage" of that weapon.  For example our 28.63-36 sword has an average damage of 58.45, based upon 10% critical hit rate.

Step three: BS/2 than calculates the average damage of a perfect and fully tinked up and similarly imbued sword: 24-40 sword with 9 tinks in iron/granite and comes up with an average damage of 68.76.

Step four: BS/2 subtracts our sword's average damage from the perfect sword's average damage and multiplies the result by 5%.  This is by how many percent our sword is "off" from perfect, it is the imperfection percent.  Resulting DmgGrade is given as a difference between 100% and the imperfection.