The short answer is because light is diffracted more due to smaller openings, leading to more interference and hence bands that are closer. Therefore, when the aperture is widened, one could expect the light rays to be diffracted less (i.e. their diffraction angles are smaller) and therefore interact less, leading to closer fringes. When the aperture is sufficiently wide (width >> wavelength), the light rays just pass through without being diffracted at all. For a more detailed explanation, I suggest looking up "hyugen's principal" in respect to single slit diffraction.
A useful tool in determining correlations between phenomena is to look at boundary cases. In this case, just recall that light passing through a large aperture doesn't seem diffracted at all!