The best work that I know is some recent research by Ray Browning and Rodger Kram in Boulder Colorado. In a May 2005 paper they reported that obese women used about 11% more energy per distance travelled than normal weight subjects. Browning and Kram wanted to learn if obese people adopted different walking techniques to compensate for the extra energy they must expend for walking. In a February 2006 paper they report that obese men and women expend about 10% more energy walking than normal subjects and that obese women require about 10% more energy to walk the same speed as similarly obese men. Kram and Browning were surprised to find that mass distribution (thigh mass/body mass) was not related to the net energy expended, but body composition (% fat) was. Another interesting finding was that, for walking a set distance, slower walking speed tends to burn more calories on average so they recommend longer slower walks. They are continuing their research to learn if obese individuals adopt unique walking strategies to move more effectively.
Incidentally, Ray Browning is also a very famous triathelete who won seven Ironmans before he returned to university to do his PhD.