Thickness, also known as caliper, speaks for itself. "Main" or bulk is the ratio of thickness to weight (grammage).

"PAPET. Main (d'un papier). Valeur arithmétique exprimant le bouffant et qui est le quotient de l'épaisseur d'une feuille de ce papier exprimée en millièmes de mm. par le grammage"
http://www.cnrtl.fr/definition/main

"Bulk is a measurement of paper that often determines what type of printers can handle it. Bulk is used to measure the ratio of paper thickness to its weight in cubic centimeters per gram. The formula for bulk is thickness (mm) x basis weight (g/m^2) x 1000. Basis weight is another property of paper you must know to determine bulk. Basis weight is also known as "grammage" and measures the weight of paper per unit area, expressed in grams per square meter."
https://sciencing.com/determine-paper-bulk-6636801.html

"Because of the higher bulk of 1.5 and its stiffness, Amber Volume allows you to choose a lower grammage and save money due to a reduced total weight."
http://www.arcticpaper.com/en/Amber-calculator/

"main f. IMPRIM. papier bulk"
https://books.google.es/books?id=_9oqBgAAQBAJ&pg=PA425&lpg=P...

"Bulk
Bulk expresses the specific volume of a material. Bulk is the inverse of density.
bulk = 1 / density = (cm²/g)
In the paper trade bulk is a more commonly used measure than density to indicating the "compactness" of paper. Bulk can be calculated by dividing the thickness of a sheet by its basis weight. In some connections, bulk is used to express the thickness of paper or board according to the following equation:
bulk x basis weight = thickness

For example:
Bulk...........Basis weight...............Thickness
1.3..............100 gsm.................130 microns
1.6...............80 gsm..................130 microns

This is done particularly when choosing bookprinting paper and packaging."
http://www.yes-paper.com/index.php?yespaper=yespaper-paper-g...