Just glared over all responses and one thing always amazes me in these discussions... nobody talks about angle of attack.
Best glide is a result of a wing characteristic, aka Cl/Cd curve, polar curve,... The wing will create best glide at a certain fixed angle of attack. As long as you don't change the wing profile, this angle of attack is a fixed value. To me, one of the most beautiful words in aviation is "finesse"...
Then you look at the aircraft and I guess it's easy to understand heavier weights require higher speeds for to fly this optimum angle of attack.
I've never been a military pilot, but always envied aircraft with AoA indications. Climbing and descending would be so much easier... and safer.