Could the slight extra thickness and weight be causing this?
Most definitely. That doesn't mean that it will, but it certainly could be the issue.
All the various docks are subject to manufacturing variations. They don't have to meet an MFi spec. So any given dock's design or build quality could be a small issue. I think Apple said the difference was .25mm and that would be enough to make a difference in some docks. Even setting the puck in a stand could make a difference.
My Griffin dock uses a rubber O-ring to keep the Watch from spinning. Every so often I have to clean it or the Watch will to spin. (Not on it's own, obviously. LOL
Try cleaning the mounting surfaces or adjusting the charging puck's depth in the dock. It may be some docks will just fit better than others.