Fine yarn, often used for weaving, comes measured in the New metric, or Nm system. This was rather confusing at first but I have now figured out how this converts to knitting weights.
The weight is expressed as two numbers, with a backslash separating them, such as 2/30, 2/60, 1/30, 1/15, etc. Sometimes these two numbers are reversed.
The second (and larger) number refers to the meters of yarn per gram of a single strand of the yarn, so 30 indicates that each gram of the single strand of yarn is 30m in length.
The first (and smaller) number refers to the ply, so how many single strands have been wound together to make the finished yarn. This does not necessary indicate the thickness, as fatter yarn can be made as single ply, and very thin yarn can have several plys.
So, a 2/30nm yarn is two strands of 30m/g yarn, plied together, giving 15m/g for the finished yarn. A 1/15nm is a single strand of 15m/g yarn. A 100g of either 2/30nm or 1/15nm yarn therefore is 1500m long.
1/15 and 2/30nm are approx. laceweight.
1/60 is approx. cobweb weight.