It might be easier to just use an ability which reduces the player's encumbrance at various periods, then restores them when the ring is removed. It's a little more difficult to work with than several burden abilities, and would work by lowering the maximum that a player could carry, not increase the weight of anything they had, but might be a bit cleaner than swapping out multiple abilities.
http://cs.elderscrolls.com/constwiki/index.php/ModActorValuehttp://cs.elderscrolls.com/constwiki/index.php/EncumbranceBut really though, the effect probably wouldn't be noticed by anyone since almost everyone uses a mod or something else which allows them to carry more. Even as far as burden goes, what would seriously inhibit most people (50-100) would, and is, rather meaningless when people have carry limits over 2k. This is because the spell effect just adds to the player's weight, rather than affecting it by percentage (like it was in morrowind). And there is no real way to combat this since the player may be achieving that additional carry weight because of changed game settings, having alot of strength, or through scripting.
And from a LOTR perspective, the ring didn't become heavier when used.