Etymology of "typeface Weight"

OED has a draft addition from 1993:

Typog. (a) The heaviness of a fount of type, determined by the thickness of strokes in the individual sorts; (b) the degree of emphasis or blackness of a typeface.

1771 P. Luckombe Hist. & Art of Printing 239 A Fount of Roman Letter, of what Body or Weight soever, is constituted of Lower-case Sorts, Capitals, Double Letters, [etc.].

(along with several other later citations)

It is true that individual letterpress letters would be very slightly heavier if they printed a bolder letter [at the same size], but it's unlikely to be a substantial difference.

OED has a related entry for weight, which I suspect is at its root:

2. Associated with measure and number, esp. in figurative expressions referring to due proportion.

The earliest citation for this use (which would later be applied to type) is from c1250.