bjk--
Has testing been done? Yes! Can I provide exact references and results--no!
Every bowyer's bow will handle SUPER light arra's in a different manner. Also, that same bowyer's bows, to the same spec's, may shoot that arrow fine from one bow, and blow up the next...
Why--because wood is wood, and grain structure is provided by nature...therefore hard to say some subtle grain defect won't become stressed to failure by the extra "snap" of the limbs without enough load (heavy-er arrow) to absorb the energy and impact from the string.
Look at oly limbs--they're shooting synthetic cores for a reason--stability, uniformity, consistency, production controls, and strength...
So yeah--the statement currently in vogue of "shooting arrows lighter than 9gpp will void your warranty" has some CYA built in...as those bowyers also have to pay for liability insurance!
Now for hunting situations--the heavy arrow will absorb more force, thereby attenuating vibration that would otherwise be induced into the limbs/riser--i.e. "hand shock".
That absorbing property also reduced noise, as the decibel level will be reduced if that energy isn't transferred back into the bow and the shooter's arm.
As for as penetration, you'll have to take that up with Dr. Ashby and his associated, quantifiable testing and reporting that he has so graciously provided for us...
Take Care,
Marc