Wikipedia says this about font weight:
The weight of a particular font is the thickness of the character outlines relative to their height.
Seeing this from the point of a mathematician, the outline is by definition a zero-width closed path. It also does not specify whose character's outline(s) is/are meant. If one looks at the stem of the ‘H’ in the example graphic, its ratio is ~0.30 (for weight 9), and ~0.04 for weight 2. Considering the entire glyph, its ratio is ~0.91 and ~0.77, respectively.
Given any glyph in such an image, how does one determine the thickness values 2…9? (or 100…900 in TrueType dimensions)