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I belive it has to do with the AOA and at a higher weight your gonna be at a higher angle of AOA, thus you will stall out before damageing anything. Let me know if i am on the right track!
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Yup, thats it! Va corresponds to an angle of attack, not an airspeed; that's why it changes with weight.
Here's an example: Say your airplane stalls at an AOA of 18 degrees. It's gonna stall at 18 degrees regardless of weight or airspeed. Since Va corresponds to an AOA, not a speed (and it is the best AOA to fly in turbulence since it provides the best margin between stall and overstress), your AOA at which Va is reached will change with weight. A heavy loaded airplane will need a higher AOA to maintain the same airspeed as a lightly loaded airplane simply due to the fact that the wing must support more weight.
As for why Va is an AOA and not a speed, here's another example: Once again, assume the critical (stalling) AOA is 18 degrees. You're flying at Va, 100kts, at 5 degrees AOA in turbulence and hit a 2G vertical gust. The wing must now support twice the weight to maintain altitude so the AOA increases to 10 degrees. Now you hit a 3.8G gust, the AOA goes all the way up to 18, and you're thankfully stalled before you can overstress the plane.
Now push your passenger out the window and see what happens. You're lighter and only need to fly 95kts to maintain 5 degrees AOA. But you keep it at 100kts (previous Va) to see what happens: since you're lighter, the wing needs less AOA to support itself at the same speed. So you fly at 100kts at 3degrees AOA. Now you turn around and hit that same 2G updraft, increasing your AOA to 6 degrees. That 2G updraft increases to 3.8Gs, and the plane now flys at 15 degrees AOA. Notice how the plane is still flying at 3.8Gs, not stalled. NOW that 3.8G updraft is increased to 5Gs, the plane needs to support itself 5 times over, it reaches 18 AOA and stalls. Here you can see both why flying faster than Va would cause damage before a stall, and why Va increases with weight.
The only reason we fly airspeeds instead of AOAs is because there's no AOA indicator in the plane. I think larger jets have turbulence penetration speeds, not Vas, maybe someone can explain why THAT is.
I hope this made SOME sense (and wasn't TOO long); Machado's private book has a VERY good explaination (along with great pictures) if you're looking for more.