The brightness of extended objects (galaxies and nebulas) is proportional to the square of the exit pupil. Therefore, a low power 4mm exit pupil (42 = 16) is four times as bright on galaxies and nebulas as a medium power 2mm exit pupil (22 = 4). To put it another way, twice the power results in one-fourth the brightness on the faint fuzzies outside our solar system.
On the other hand, the brightness of a point of light (a star) is a function of the aperture of your scope – not the exit pupil. The bigger the aperture, the fainter the star you can see. Stars do not get dimmer as a scope’s power increases and the exit pupil gets smaller. Extended objects do, however, and the sky (the most extended object you’ll ever see through your scope) becomes progressively darker as the power goes up. The result is that faint stars are usually more visible at higher powers, as the contrast between the unchanging star brightness and the progressively darker sky background increases.
From dark sky sites, a 5mm to 7mm exit pupil is best for observing Milky Way star clouds, open clusters, large nebulas such as the Veil, etc. From mildly light-polluted suburban sites, a 3mm to 4mm exit pupil improves the contrast of these large-scale objects by darkening the light-polluted skies somewhat without overly dimming the objects themselves.
A 2mm exit pupil most closely matches the area of highest resolution in your eye and gives you good detail for planetary, lunar, and globular cluster observing. The sharpness of those details is likewise improved by a 2mm exit pupil, as a smaller exit pupil minimizes astigmatism at the edges of your dark-adapted eye. Also, the visibilty of small galaxies and planetary nebulas is often enhanced by the darkening of the sky background with a 2mm exit pupil.
A 1mm exit pupil gives you maximum planetary detail and is excellent for splitting binary stars. A 0.5mm exit pupil is useful for splitting close double stars, but only during very good seeing.
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