I don't really worry about heavy or light...I tune my arrows and use whichever shoots the best. But since we are discussing this, I thought I would throw this in for something to think about. I didn't write this so I have no argument either way. Here ya go:
What do an arrow and a missile have in common? The answer lies in "spinning mass" The greater the mass the greater the angular inertia.
To compensate for yaw, pitch and roll a missile's orientation with respect to external co-ordinates is maintained by a gyroscope. Instead of tipping over it moves forward in a circular motion, in a fixed direction given by its spin axis.
Rotational Inertia is the rotational counterpart of Newton's First Law of motion, "An object will continue to spin in a given direction unless acted upon by an external unbalanced torque."
In a missile, if an unbalanced force is applied the gyro will begin to move the missile at right angles to the force. This motion is called precession.
When a football flies through the air its natural tendency is to tumble (rotate end over end) icreasing air resistance.
If the thrower puts spin on the ball (hence giving the ball angular momentum) the ball behaves much like a missile with a gyro and an arrow with feathers does that even better, giving it spin, hence keeping its point axis always in the direction of motion, reducing resistance and increasing the distance travelled.
Hence, the Turks shooting toothpicks have never been equalled pound for pound.
In an arrow this angular momentum caused by spin pushed by the Ek of the bow is critical in its path through the atmosphere and the deer's flesh.
A heavy arrow has greater angular inertia, therefore requiring greater Ek from the bow. It follows then that a lighter arrow with the same Ek, out of the same bow will have a much higher angular momentum and hence will travel farther and straighter.
It also follows that the use of large feathers create a tremendous amount of drag and this creates an even greater increase in angular inertia. Thus requiring heavy poundage to create equivalent forward motion.
The earth spinning on its axis acts much like a 'gyro'. The point, N-axis always aims at Polaris, inspite of the much heavier gravitational pull of the Sun, the moon and all the other celestial bodies in the universe. Unlike very stiff carbon shafts the slight precession of the earth is caused by the unequal distribution of mass.
A heavy arrow will hit with a higher force but much more Ek is necessary to drive its rotational momemtum. Whereas, a very LIGHT STIFF arrow with equal Ek will fly better, do to its much higher angular momentum and can get the job done better with even less poundage. Not to mention the fact that less poundage equates to a better bowman. As long as we are not hunting Tyrannosaurs.
Arrows are not bullets and do not kill by expansion and crushing. It takes very little force for a two blade titanium broadhead with molecularly sharp edges to go through flesh.
In Physics this problem requires many and varied formulae to prove, some 18 altogether.
The basic one's being.
Ek = 1/2mXvsquared (linear) Ek(rotational) = 1/2I(w)squared (angular)