Torque is force times diameter. (You may remember this from elementary school science, where two objects with mass of 1:2 will balance with each other if the see-saw's length is 2:1, thus equalizing torque). Given a torque at which a joint will break, more diameter means less force is needed to create the torque. So, with longer BSL, the binding needs to release at a lower force applied to it.
The weight and height are a bit more complicated. With two people doing the exact same thing, with greater weight or greater height, more torque is applied to the joints and more force is applied to the bindings; at the same DIN, taller/heavier people is more likely to release prematurely. Now, one may wonder about the fact that the heavier/taller person is then more likely to be injured with the same movement, since they will be facing more torque on their joints. Why don't they? Because their joints are already accustomed to stronger force--they have more muscles and ligaments around the joints (joints have no inherent strength in themselves, and derive their strength and resilience from muscles and ligaments)--so they will break at a higher torque. So the higher DIN setting works fine.
Of course, heavier/taller does not mean stronger joints, just like 50+ does not mean weaker joints. In other words, the weight/height presumption is actually just as arbitrary as the age 50 thing. Just a guideline.
People who ski all the time have more muscles around their joints, and can tolerate higher torque. Same with aggressive skiers. It's not that you want higher DIN because you are more aggressive; it's that your body can become tolerant of higher torque if you are consistently aggressive. If you are out of shape and try to be aggressive, you will get hurt at higher DIN.
The DIN standard has been incorporated into ISO 8061 (I couldn't find the original DIN standard number). It is still called DIN out of habit.