Although Floris made a clear picture involving only vertical forces, this picture is mostly useful when carrying washing machines or large chairs, where the 'height' of the object is more pronounced.
However, you will find that, even when the object is mostly flat, the bottom person will carry most of the weight. The key here is the direction of the forces involved.
You will find that it's very difficult to lift a couch underneath you, 'tugging' it upwards. Instead, the top person will apply force in the direction that does not require any tugging (especially when you can't get a grip): perpendicular to the object. All you do, is offset the torque gravity incurs on the couch, where we take the bottom person as the pivot point. In the image above, the torque is provided by the component of gravity perpendicular to the couch (green arrow).
Since the top person is twice as far away from the pivot point as the center of gravity, he will only need to apply half of that component which was already less than the total gravity - i.e., much less than half of the total gravitational force. The top person has the easy job, although usually in a very awkward position.
The bottom person needs to account for the rest of the upward force required, along with a small horizontal component to make sure there is no horizontal acceleration (blue arrows) - i.e., a lot more, which is why being the bottom person is the heavier job.