I don't think it's completely true. Higher weight increases the speed at which the glide ratio is optimal, and drag (parasitic drag in particular, unrelated to generating lift) increases with the square of speed. Basically, flying faster wastes more energy. That effect is going to dominate at some point, probably about 120 km/h or so with a typical glider. At 200 km/h, the glide ratio is garbage (but it's fun). I have flown gliders.
I'm not sure if simple descriptions of the phenomenon that glide ratio is independent of weight are missing an asterisk or if I'm just wrong...
A decent glider has a ratio of 1:40, an A320 1:17. Is the A320 a "bad plane" or is it optimized for higher speed with the corresponding worse glide ratio? (It also has engines that produce a lot of drag when gliding)
On another hand, there are CFIs, the FAA, books, etc.
I've only found one search result that agrees with you, so far, and at least a dozen that disagree, but the one that agrees with you has no math in it, and the ones that disagree mostly seem to depend on the same source info, so that doesn't feel conclusive in either direction.
The Wikipedia page on lift-to-drag ratio also believes weight does not matter to the ratio.
As a side note, your 200km/h example also sounds like it's just not the correct angle of attack or airspeed for the aircraft, so I'm not sure if that example applies?
As a separate reply, I'll add that I think finding where/if this breaks is pretty academic.
Eg: you wouldn't build a glider out of heavy material that gives you huge speeds but also huge sink rates.
So I think the entire glide ratio conversation mostly fits in the "your plane is fully loaded" vs "your plane is empty" scenario, and the point is that your best glide ratio will be constant, but you'll be gliding at higher speeds if you have more weight.
Gliders utilize Laminar profiles, while airliners use turbulent profiles.
The Laminar profiles perform better, but only when uncontaminated (no bugs or rain). Contaminated turbulent profiles perform better than contaminated Laminar profiles.
Since regulations state that you should carry fuel for the worst case scenario, it does not yet make sense to design airliners with Laminar profiles.
Naturally, manufacturers are looking for ways around this.
There is an asterisk that you have to be at the right glide velocity, but yes: they'll have the same glide angle. The leaden one will just go significantly faster. And yes, it does sound unlikely. That's why I made my previous comment.
Thanks for the links. Weight may cancel out of the equations, but (being a bit pedantic) I suspect 'glide angle in independent of weight' only holds up to a point. Taking things to extremes, if the glider is heavy enough that you are going to have to go supersonic then I suspect a lot of the assumptions become invalid.
NB/ spherical cows are unable to glide in a vacuum.
Make a paper airplane and drop it. It likely won't go much further than your feet. Throw it gently and it will go some distance. Throw it harder and it will go further. Glide ratio is the horizontal distance over vertical distance. The vertical distance is the product of (lift - mass)*t^2 where lift is a function of the shape of the wings and the airspeed. So given a higher mass and the same lift, the time to hit the ground will be less when the glider is dropped at 1000ft. Increase the airspeed and you'll have more lift to negate the higher mass. The increased airspeed also means your horizontal distance will be covered faster. The lead glider will travel the same path as the normal one but will be going a lot faster. The reason why gliders are built as light as possible is reduce the work required to lift them, the speed at which to release them, and the interia required to turn them. You also have the benefit of being able to land them at a lower airspeed without injury.
I assume it is a relevant enough concept to flying an aircraft (which also happens to be the context of TFA) that you learn about it while flying.
I guess another thing worth noting is that "glide ratio" isn't the same as "gliding" in the "flying a glider" context.
The space shuttle is probably the most famous glider, and was described as "a flying brick" and getting it to the ground at the right spot was very much a matter of glide ratio. Worth noting the space shuttle's speeds started off as hypersonic.
By comparison, a typical glider's built to be able to take advantage of air currents to regain altitude, and I'm not sure how weight affects that.
Weight affects speed with minimum sink. That affects the diameter of the circle you fly. Since thermals have more lift towards the center (assuming perfectly circular thermals), you are not able to circle in the strongest lift. So you climb more slowly.
You can glide faster with the same L/D, so that might be worth it if you try to optimize for speed.
(Don't worry, reader, I never intended to get a pilot's license.)