RE: how light is too light.
All things other than weight about an arrow being equal, such as the diameter, length, fletching, spine, broadhead, etc..., shot out of the same bow the heavier arrow will penetrate more than the lighter arrow. It will have slightly more KE and a good bit more momentum. There is a point of diminished returns on both sides of the weight issue though.
To be honest it does not take a whole lot of energy to blow right through a whitetail deer. So who is to say what is too light. I will tell you that if he were to ever go after larger and tougher animals that he would want to use a heavier arrow.
On another note the lighter the arrow the more energy left over that your bow has to get rid of in the form of noise and vibration. Another thing to consider is that the lighter the arrow the more abuse your bow is taking primarily in the limbs.
Personally I use to be a speed freak and shot 380-ish grain arrows but soon realized that quiet is far better than speed any day. You didn't say what poundage his bow was at but I like to keep my arrows weighing between 6.5 and 7 grains per pound of draw weight. For a 70 pound bow that is between 450 and 500 grains. I feel this is a very good compromise between speed, noise, vibration, and energy. When I began shooting these heavier arrows the noise went way down and so did the bow jump and hand shock.
His arrow is far too light for me personally but if he likes them then let him shoot them..