When we think of the wing loading as simply a descriptive parameter then it is hard to see why it would change. We should note however that the wing always generates lift normal to its chordwise datum line. A little geometry shows what could be regarded as an increase in effective wing loading.

As the AOA increases the wing's lift vector tilts forward away from "up and down" but only the component of this vector along the "up and down" line actually contributes to "lift" defined as the force holding the weight of the plane up in the air. This component is smaller the greater the AOA. That is, less of the work done by the wing is holding the plane up, so we can regard this in a sense as increasing the loading of the wing - the plane has to fly faster to generate the lift needed to remain at a constant altitude.

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Another way of thinking of this is that the cross-sectional area of the wing as viewed along the "up and down" axis decreases as the AOA moves away from 0 degrees. Since the mass of the plane is constant (neglecting fuel consumption etc) the wing loading at that moment is effectively greater because the wing is generating "lift" as if it had a smaller chord.