To bump a hella old thread, largely for future searching purposes:
While pretty much all of the hypotheses surrounding narrower tires are valid, it is important to note that the contact patch is technically the same total area for either style of tire, at the same air pressure.
If you assume 1000 lbs on each corner of the vehicle, the total force each tire exerts on the ground is 1000 lbs. At 10 PSI in the tires, that would require 100 square inches of tire surface to be touching the ground, regardless of the shape of the tire. A wide tire will have a shorter and wider contact patch, while a narrower tire will have a longer and skinnier. But, again, they will technically have the same surface area.
As has been addressed and implied, narrower tires will have a longer contact patch. It is indeed this longer contact patch that allows for the mechanical keying described above, where going over a ledge or other lateral obstacle the tire is better able to "reach" beyond the obstacle to "key" and maintain traction.
With soft surfaces, narrower tires will tend to laterally displace more media as they travel, causing a tendency to see the "sinking" we have discussed. They do not sink deeper because the overall patch area is smaller; again, it is only because the narrower profile causes them to push more media to the sides relative to the area of the contact patch.