From the Wikipedia page's sources, it appears that aerodynamics is the main reason that outer parts generate less lift.
The second apparent advantage is aerodynamic, and has to do with the drag penalty associated with lift,the so-called induced drag. Induced drag cannot be eliminated, but it is at its minimum when the spanwise distribution of lift is elliptical. Equating area distribution with lift distribution (a big conceptual leap, but let's make it for the time being), the argument goes on to assert that a rectangular wing deviates greatly from the elliptical ideal, especially near the tips, whereas a moderately tapered wing or a double-tapered one, with a straight inner section and a tapered outer section approximates the ellipse much more closely.
This Wiki page on Lift-induced drag describes how rectangular wings produce stronger wingtip vortices, which in turn lead to less effective lift generation.
When producing lift, air below the wing is generally at a higher pressure than the air pressure above the wing, while air above the wing is generally at a lower than atmospheric pressure. On a wing of finite span, this pressure difference causes air to flow from the lower surface wing root, around the wingtip, towards the upper surface wing root. This spanwise flow of air combines with chordwise flowing air, causing a change in speed and direction, which twists the airflow and produces vortices along the wing trailing edge. The vortices created are unstable, and they quickly combine to produce wingtip vortices.
Wingtip vortices modify the airflow around a wing. Compared to a wing of infinite span, vortices reduce the effectiveness of the wing to generate lift, thus requiring a higher angle of attack to compensate, which tilts the total aerodynamic force rearwards.
A rectangular wing produces stronger wingtip vortices than a tapered or elliptical wing, therefore many modern wings are tapered.
Similarly, for a given wing area, a high aspect ratio wing will produce less induced drag than a wing of low aspect ratio because there is less air disturbance at the tip of a longer, thinner wing. Induced drag can therefore be said to be inversely proportional to aspect ratio.
This NASA study goes into detail mathematically and describes why the spanwise distribution of lift must be elliptical to minimize drag.