Basically, since a lighter aircraft stalls at a slower indicated airspeed it will reach it's load limit at a lower airspeed as well, hence Va decreases with as weight decreases.
I am at work and cannot address this now, however there is some erroneous thought process here. I will be home later and elaborate talk to you all then.
Edit: from here on added.
The erroneous thought process lies in the bold lettering as noted above is not so much wrong (because it is in fact true), it however completely leaves out the why. First off all v-speeds go down with weight, each for different reasons and just because one goes down for one reason doesn't mean the others have to go down, sure they do, but the reasoning is still different.
Edit: added first why and bolded the second for clarification, I am not argueing they are unrelated. I am saying the reasons for each are unrelated.
For example, the reason
why stall goes down is completely unrelated to the reasoning for
why Va goes down with weight, for stall we have this:
First it is known that lift must overcome weight to maintain flight.
Now we must know how you determine lift:
In the above formula L = lift, p = air density, v = velocity, a = area of the wing, and Cl = coefficient of lift found by (Cl = 2 * pi * angle (in radians)).
Now let us assume that aircraft a weights 2000 lbs and b weights 2500 lbs and both stall at 18 degrees and have are the exact same aerodynamically. So we will fly each aircraft at exactly 18 degrees angle of attack maxing our Cl and leave that as a constant, we will also leave density and wing area as a constant. All that is left to adjust the formula to raise or lower the value of L is velocity, this is why stall speed decreases. Since aircraft weighs in at 500 lbs less than aircraft b than aircraft a can maintain sufficient lift (2000lbs) at a slower airspeed than aircraft b w/o exceeding critical angle of attack. Aircraft b to fly at the same speed as aircraft a and get enough lift would have to raise its angle of attack or increase its airspeed, since raising AOA will go past 18 degrees (our critical for this simulation) then aircraft b will stall if it tries to do that.
As for Va that has already been discussed and the above mentioning of it relating to flying at a lower AOA and being further from critical are in fact the reason Va changes with weight. It isn't that it overloads at a lower airspeed and in fact the Vg diagram does nothing to display Va changing with weight, it overloads at a lighter weight at a lower airspeed because it is further from critical angle of attack and because its further from critical AOA that gives you that much more "time" shall we say, to bring the aircraft beyond its load limit. The post above mine is a good example but relates to speed and not weight which can cause some confusion but the idea remains the same. A heavier aircraft will need to fly at a higher angle of attack (see formula and how you find Cl) to maintain enough lift to overcome weight, because this higher AOA is closer to critical Va can be reduced.
An interesting add here that I think all CFIs should know is thie structural limits of an aircraft are based on:
1) Symmetrical loading (pulling in a turn is different then straight and level!) At Va in a turn the outside wing is faster than Va...inside slower...
2) Progressive loading (snap stalls at Va might leave you without a wing)
3) Changes based on materials (not really something a pilot needs to worry about)