The Ring of Burden is a ring that was made by Falcar, the head of Cheydinhal's Mage Guild. At 150 pounds, it is ridiculously heavy and serves no purpose. The Hero is required to retrieve it as part of the "Cheydinhal Recommendation" quest. It is a joke of a ring that caused the death of another Mages' Guild Initiate, Vidkun, who drowned in the well behind the guildhall while trying to retrieve it. Deetsan says that Falcar made it as a "sick joke."
The only semi-practical use for the ring would be if you were able to place it on someone else, in order to "burden" them with it. 150lbs is a lot of weight, and since NPCs would not not remove it, its effects would be permanent. It cannot be placed on a person by either reverse pickpocketing them, or by paralyzing them and then placing it on their person (while in sneak mode). Attempting this prompts the in-game message "You cannot place items in a container while pick pocketing" only 0-weight items can be reverse-pick pocketed onto NPCs making this ring totally useless. Though 150lbs is a lot of weight to carry around, "feather" effects can be used to allow the character to carry more. The ring can also be dropped and then grabbed and carried around in order to negate its weight.