During a review of the V-speeds for an airplane I've never flown before, my
instructor asked me about glide speed vs. weight, and total glide distance.

I got the glide speed vs. weight part right, but the distance part seemed
counterintuitive - that the total distance covered (by flying at the correct
best glide speed for the weight) would be the same, regardless of the
weight.

Can anyone explain this so that it makes sense?