A weight (5kg) 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," he/she must take enough weights to equal 4 kg (40 - 36 = 4). In this case, the player cannot take a weight that is 5 kg, so he/she must take either four 1 kg weights or two 2 kg weights, which are also 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.