Why does an airliner have a shallow descent when heavier, opposite to gliders with ballast? Gliders utilize water ballast to, among other things, descend faster:

But sometimes you need to get down fast: This is when water ballast is added.

In airliners however, the heavier the plane, the shallower the rate of descent.
Why is that difference? What is the physics involved?
Some 737 figures can be found here. And from the Airbus performance publication:

1.3.3. Weight Effect
Green dot speed (minimum gradient) is a function of weight. In the standard descent speed range (from green dot to VMO), the rate and gradient of descent magnitudes are reduced at higher weights. [emphasis added]


For the site readers based on some comments:
Descent – does not refer to landing or approach, rather the idle-power descent from cruise in clean (no flaps, speed brakes, or landing gear) configuration. The heavier an airliner, the longer it takes to get down.
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.