If stars appear as points, why are some stars big and some small in different images?

If stars are unresolved points, even in the largest telescopes, why do bright ones look bigger than faint ones?

Our eyes are amazing instruments, but they’re limited by physics and biology. When starlight enters an optical system with a circular aperture, such as a telescope or a human eye, the image that forms is not a point but a round spot that fades from center to edge. This is true even for perfect (“diffraction-limited”) optics, in which case larger apertures yield smaller, sharper disks and, therefore, higher angular resolution.

In principle the dark-adapted human eye could focus starlight into a spot about 40 arcseconds across, with a bright core less than half that size. The density of light-sensitive cells in the retina actually would permit a naked-eye angular resolution in this range, but imperfections in the eye bloat star images much further and distort their shape. When you gaze at the constellations, every star produces an image that’s the same size, but your retina isn’t sensitive enough to respond to the outer parts of those images except for the brighter stars — which therefore look bigger than the fainter ones.

— Richard Tresch Fienberg