I've been watching this thread for a while now. It reminds me of a discussion that I was involved in during college concerning aerodynamics, friction, and efficiency. I feel that it's time to submit my 4 1/2 cents...
The textbook answer is that weight is not a factor when considering simple horizontal linear motion in an absolutely frictionless environment. If you are changing the elevation of the item then weight (mass) is a factor because you are adding or removing potential energy. One of the laws of physics is that energy cannot be created or destroyed. That being said, if you return to the same location, the vertical motion of the item has had ZERO impact on the energy used because it is in the same potential energy state as it was before you left.

What makes things inefficient is friction.
Friction is a funny thing...it comes from places that you would least expect. For example: describe the rolling of the rubber on the road, distortion of that rubber to conform to the road surface, flexing of the sidewalls, motion of the air within the tire, airflow around the tire, texture of the tread pattern, does it make a noise (noise is a "loss" of energy), ANYTHING out of balance, is the valve stem long or short, does the valve stem have a cap...

Pretty complex already and we haven't even started to address the metal parts. Many of these things can be controlled or adjusted to an extent. Air pressure can be raised, hence less flex, smaller contact surface. The formulation of the rubber in the tire, harder surface, "slick" to airflow, etc.
However, in the real world, friction cannot be completely eliminated. Assuming that you could create a perfect frictionless exterior to your teardrop
(now you can forget that beautiful paint job, it just won't stay there) ... when you pull it through the air, the air will have to move out of the way, let the trailer pass, then return back to where it was previously. This creates friction. Any motion that the air has after the trailer has passed has robbed even more energy from the system. Here is where aerodynamics comes in. The whole idea is simply this ... allow an object to pass through the air and return that air back to a motionless state instantly after the object has passed.
(If you can figure this out, I can make us both rich
) Aircraft fly by intentionally creating a downward motion to the air as they go by. This is what creates the lift that keeps them in the air. These things can also be manipulated to an extent ... smoooooth surfaces, gradual transitions, "sharp" trailing edges, equal distances for the airflow around the object, etc.
To make a long story short ... in the real world, weight is a factor, but it is a small one, and it it a function of the "friction" that is created by that weight, i.e. the flex in the tires, etc. Aerodynamics helps, replacing the grease filled hub with a "wet" one using lightweight oil would help, rounded corners, no exposed handles, minimize frontal area, get rid of those sliding magnets in the braking system, reduce the speed of travel, etc. There are literally limitless ways to improve efficiency, but each comes at a cost and each improvement, unfortunately, will be less and less cost effective. Eventually there will come a point where further improvement is not worth the effort ... I leave it up to you to decide when you reach that point.
Corwin