Why does an airliner have a shallow descent when heavier, opposite to gliders with ballast?
If you can forgive my limited Paint skills:

It's the variable/constant speed that makes the difference.


Weight changes endurance (time to ground) and not range (distance to ground) if speed is adjusted to match the new weight.
Weight changes the speed for best L/D, but does not ever change the best L/D ratio (and thus best range)


For gliders (which are adjusting speed to new weight): 

ballast allows them to fly faster while maintaining best L/D. Pilot will increase speed to keep same (best) gliding ratio, albeit at an increased descent rate (fpm). You get there faster, in an increased rate, but same gliding distance (to the ground eventually).



For powered airplanes (flying at set speeds regardless of weight): 

pilots usually descend from cruise at fixed airspeed, usually much above the best L/D. Higher weight means the aircraft is much closer to best L/D speed, so the flight path is much shallower. You get there in the same time, but you will be much higher when heavy.

Or if it is easier to think this way, a light aircraft is a lot further away from its best L/D speed than a heavy one, when flying an approach. Naturally this makes the light one descend more steeply.

Note that this all refers to a normal descent from cruise. Final approach speeds, just before landing, are indeed corrected for weight in a large airplane, and heavy ones will indeed have a higher Vref and land slightly faster.