Leila Benali buys the six papers from the mills, and the question she hears most is which one is thickest. Weight is the figure on the pack, in grams per square metre. It tells you how much a square metre of the sheet weighs, not how thick it is.
Two papers of the same weight can feel different in the hand, because the fibres, the pressing and the finish change how much room the sheet takes. That is why the counter asks you to hold the sheets to the window before you choose.
The shop keeps six papers so the comparison stays in the hand: Airmail Bank at 45 gsm up to Cotton Rag at 300 gsm.