There was something like this in Skyrim: If you collected too much gear, your character would walk and react way too slowly (think about Link trying to get somewhere while wearing the Iron Boots the entire time; it would work like that). In order to go back to a normal pace, you had to make the character discard a number of the items he was carrying. I don't see this sort of thing happening in Zelda, though it's always prone to happen.
Now to answer the question directly. A concern I'd have with this is how Link would cope with this happening. In Skyward Sword he could go to Skyloft's bazaar and visit the Item Check in order to drop off gear or take it along for the journey. But there was only one station that he could do that in. Just suppose that if SS employed the weigh and mass scenario that you present, but only had that single Item Check back in Skyloft... It sure would suck if we'd collected an excess amount of equipment in Faron Woods and had to trade a good portion of that in, because Link was moving like a slug to begin with. Although I might be complicating the usage of this concept to some degree, again, under the supposition that you couldn't drop anything, this would only extract frustration from the player.
The way I can see this working is by having multiple "Item Checks" conveniently situated within the separate regions of a new Hyrule—or of an entirely different land. A Castle Town and various villages or small habitations would work out pretty well, I suppose. I'm not a huge supporter of this idea, because, looking long-term, I see only a large amount of complaints which might spring from its implementation. Nevertheless, Nintendo wouldn't take it up on such a large scale without creating safeties—even fail-safes—for it; otherwise I could only see them not using it, since it would be a detriment moreso than a benefit.
This isn't a bad idea on your part, but it seems very hard to accomplish, and without a barrage of criticism that would possibly ensue.
