I just ran into this, and thought I'd share it.

So I'm running around over-encumbered (well...walking around) and crossed a river. It makes sense now, but at the time it didn't occur to me that I'd sink. So be careful with that.
[Edit] Just had a thought. This might have been a glitch. Thinking back I might have drowned due to Serana. Crossing the river I got pushed up against some rocks and Serana was swimming over me, so it may just be that she pinned me down. Either way. Be careful!

I also tried walking to the nearest carriage thinking I might be able to buy a ride to Whiterun. No dice. My character would climb up into the back and just sit there. So apparently you can't even take a carriage ride while over-encumbered.
[Edit] Come to think of it, this might have also been a glitch...but I'm not sure. I'm still chalking it up to my carrying 4k lbs.

You can ride your horse while over-encumbered and fast travel on horseback... your poor, poor horse... Anyhow, this is how I move houses in Skyrim.

You can't travel back to Solestheim when you are over-encumbered

I want this fixed :s