Thought I'd share this.
I decided to do some research to help, looking at a fairly arbitrary group of 12 font families* (mostly Microsoft) and worked out the ratio between lower case thin and thick downstrokes in each case and then took an average of the 12.
It turns out that the ratios (regular:bold) varied between 0.52 (not enough difference to be effective) and 0.67 (too much difference), but the average was 0.6216.
This turned out to be almost identical to Φ (golden section)
Incidentally, this number is also the ratio between subsequent Fibonacci numbers as the numbers get big.
Since most typeface families have just a single weight in between a regular and its bold, then it follows that the thickness between subsequent weights should increase in increments of √φ = 1.27214 (where φ = Φ + 1) since, using Luc(as) de Groot's method of finding the weight optically midway between two others, m² = b² - r² (where r = regular strokewidth, b = bold strokewidth and m = optical medium strokewidth). Let's suppose r = 1 and b = φ, then m² = φ² - 1², but since φ² - 1² = φ then m = √φ.
It also follows from this that if you have a series of weights 35, 45, 55, 65, 75 and 85 (where 55 is regular and 75 is bold) that the thickness of 75 = the thickness of 35 + the thickness of 55; and the thickness of 85 = the thickness of 45 + the thickness of 65.
You've got to love maths. Any thoughts?
* Myriad, Calibri, Cambria, Constantia, Corbel, Arial, Georgia, Palatino, Trebuchet, Verdana, Helvetica and Ocean Sans