You know how Felix the Cat has a bag full of magical tricks? Well I sorta think of the same thing for Link..but instead of a bag, it's a satchel. All he does is think of the item he wants to pull out, and booyah, it's in his hand (no matter how big the item is). So the way I see it, he always has his shield, sword, cap, tunic, boots, rupee pouch, and his magical satchel.
Then of course in the LA manga (not canon) Kaepora Gaebora gave Link a fairy who would magically store all of his collected instruments for him...that's another solution.
In the end, it has to do with something magical, because items would just hold Link down all the time (such as
tWW's Megaton Boots and Skull Hammer).
-BGS