A weight (1kg) is used during the quest While Guthix Sleeps to safely exit Movario's base. There is a pile of them in the hidden room behind the painting. They are used to balance the player's weight with the weight indicated on the nearby temperature gauge.
For example, if the player's weight is 40 kg and the temperature gauge reads 36 "tickits," they must take enough weights to equal 4 kg (40 - 36 = 4). In this case, the player should take 4 weights that are 1 kg each.
There are also piles of weight (2kg) and weight (5kg) in the room.
Once the player has the required number of weights, they must be placed on the statue on the second floor of Movario's base. Only then can the player exit the base safely.
The update history project is a work-in-progress – not all updates to this topic may be covered below. See here for how to help out!