If I'm not mistaken Load, as written, doesn't necessarily place a hard limit on how much you can carry.
Keep your Load in mind—it limits how much you can easily carry. -- page 23, Beta 2.3
To me, this says that you can carry more than your Load would allow for, but that it isn't easy. Beta 2.3 also states that carrying more than your Load causes problems.
Characters are limited in how much they can carry by their Load. ... Carrying items whose total weight is more than your load causes problems. -- page 14, Beta 2.3
I would imagine that it would make for slow going through a dungeon, and present difficulties in combat and for other special maneuvers (whenever a Move comes into play, perhaps), but that it isn't strictly disallowed.
Fictionally, I see adventurers sloughing off backpacks and other extraneous items before leaping into combat or attempting to climb a sheer cliff. It just seems like those items would get in the way anyway and that most of them would seek to set down items they won't need for the immediate task at hand.
A few classes (like the Thief and Ranger) might have an interest in only carrying items within their Load so that they can always have their tools on hand no matter where they go, but who knows.
Additionally, this makes ambushing the characters even more effective for those carrying more Weight than their Load allows.
Any thoughts?