Weight is an Armour stat in Xenoblade Chronicles, and is a measure of the amount by which the armour hinders the wearer's movement. The weight of equipped armour is subtracted from the wearer's Agility. This can be mitigated by certain skills which reduce the weight of armour.
The weight stat is a combination of the armour's physical weight, bulkiness, and other characteristics which hinder the wearer's movement. For example, the Empress Mask is classified as Light Armour, but has a relatively high weight of 5, presumably because it restricts the wearer's sight.