So, assuming you have the latest
patch installed, the DK will not walk or run at all?
If you check the DK's stats in the inventory window, what is listed for the current and maximum weights?
Did you scroll down to check all the inventory categories, and make sure he wasn't carrying some heavy armour or a chest, etc? If he has a lot of food, that weight can add up, as well.
If you drop some food or equipment, is your current weight updated?
There is nothing in BD like DD's Halberd of the Rock (which drains stamina), but I suppose you could have picked up some bugged object with a large weight. Did you try dropping everything?
Could you have accidentally switched to sneak mode (right click on the ground somewhere with Sneak selected as your secondary skill), or something? A couple people have mistaken the slow movement in Sneak's crouch for being encumbered, after inadvertently using that skill.