One of my internal doors slowly swings fully open unless it's latched
closed. None of the other identical doors do this so I think it's
something to do with how it's hung, but I can't find any obvious
problems. It's a solid hardwood door (so pretty heavy) hung on two
brass hinges.

A spirit level shows that the door frame on the hinge side is
vertical, and the hinge side of the door is vertical as well. A plumb
bob made from a nut&bolt on a piece of string shows that the two
hinges are in line vertically.

Any ideas on what could be causing this?