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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)

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"Weight" is highly subjective. The designer typically designs a 'regular weight', which would be '500' in the TTF units. After that, a lighter design gets a lower number and a darker design the higher number. The full range of 100..900 is to cater for everything from Ultra Light to Extra Black.

Thus, the value only 'means' something in relation to lighter and heavier designs of the same font. You cannot look at a single font and say "this must be a Bold version".

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