Okay, I've attached an image of the math required to determine the stat-weighting for weapon damage. I'll attempt to explain what I'm doing as best I can.
First off, some variables:
CODE
d is the total damage done by an attack
P is the percent of weapon damage that applies to an attack (i.e. SS has 40% weapon damage)
D is the average damage of your weapon
AP is attack power
X is the bonus damage an attack gets (i.e. SS gets 318 bonus damage)
c is crit chance
m is crit multiplier (generally 1, but can be changed with talents/metagems)
Line (1) is the generalized equation for how much damage any one instant strike will do. You'll notice that I have left off disease multipliers, armor reduction and many other debuffs that affect the total damage done by an attack. As it turns out, these are irrelevant since they are all applied after a strikes "base" damage has been calculated.
Line (2) is an equation for the damage of an attack after we have increased the weapon damage by some value delta_D. The increased damage is here labeled as delta_d.
Line (3) is an equation for the damage of an attack after we have increased our attack power by some value delta_AP. The increased damage is again labeled as delta_d.
Lines (4) and (5) give us the value for delta_d as a function of either delta_D or delta_AP.
Line (6): Here we equate the two equations in order to determine the value of delta_D in terms of delta_AP.
Line (7) gives delta_D as a function of delta_AP. That is to say, we can enter a value for delta_AP and get the equivalent increase in delta_D.
Line (8) is the result of setting delta_D equal to one; we see that you can solve the equation for a value of 4.24 AP.
Now what does this mean? This means that for any given weapon strike, an increase in average weapon damage by 1 is the same thing as increasing your attack power by 4.24. 4.24 is, therefore, the stat weighting for weapon damage. Our story does not end there, though. This value of 4.24 assumes that
all of your damage comes from instant strikes, which we know not to be true. We must therefore take the 4.24 and multiply it by the percentage of our total damage that is the result of instant attacks. This percentage will differ from player to player and from fight to fight and is therefore not set in stone; you'll have to determine thee value that is unique to you.
edit:
All stats actually see this set of "diminishing returns", it's just not as apparent with some as it is others. For instance, since we normalize everything to attack power, you don't notice that the value of AP decreases the more you have of it. This change is instead reflected in the increase in the value of other stats like crit or haste. ArPen is unique in that it actually sees increasing returns the more you stack, but that's a result of how Armor reductions are calculated, not stat weights. Furthermore, there is nothing at all unpredictable about these diminishing returns, they can all be easily calculated using similar methods to the one I just demonstrated here.
