You must have a follower to complete this!

Speak with your follower and share items with them. You can get items out of your inventory and add them to your follower's inventory.

The follower can carry all your treasures without you getting weighed down. The items will not disappear in their inventory (although your follower can only carry a certain amount of items).

You can also join the Thieves Guild and get enchanted armor that increases the amount of items you can carry.