How does the size of the hole in pinhole camera effect the size of the image?

In a pinhole camera, the size of the hole has the same effect as the aperture setting on a more traditional camera. The size of the hole, combined with its distance from the film or sensor, controls the depth of field of the image and the length of exposure needed. Smaller holes will result in greater depth of field (to a point) and longer exposure.

To compare a pinhole camera to a traditional camera, the distance from the film to the pinhole gives you the focal length, the size of the pinhole divided by the distance to the film gives you the effective aperture which can be used to determine the exposure needed.

The reason that I included the "to a point" when discussing depth of field is that the pinhole must be in a very thin material and should be blackened in order to limit loss of sharpness due to diffraction. Diffraction also contributors to a loss of sharpness in traditional lenses when stopped down past f16 or so.