How efficient would an airliner be if it did not have to carry its own fuel?
Short answer is about twice as efficient for a mid range route,(3000 nautical miles) when based on fuel used per ton of cargo per mile traveled.

Explanation:
I will use the 737-400 as an example because I have an operational manual for it. First we need to define terms. I assume we are talking about fuel burn per something: per mile, per hour, or per payload ton-mile. Gross weight is the total weight if you set the plane on a scale in some flying condition. Max gross weight is the maximum weight at which the aircraft is considered safe to fly. Operating empty weight is the lowest gross weight achievable in a flying condition, no cargo, no extra crew or passengers, and no usable fuel. Useful load is the difference between max gross weight and operating empty weight. Payload is useful load minus fuel load and extra crew.(that is load that pays, aka cargo and passengers)

The thrust required(and thus fuel consumption) for level flight is determined by aerodynamic drag and the majority of drag is broken into parasitic drag and induced drag; parasitic drag comes from shape or texture and dynamic pressure,(basically speed if you keep the density constant) go faster get more parasite drag, this does not change with gross weight.

Induced drag is caused by the lift created by practical wing designs, for a set wing design and speed the induced drag increases with weight. So high gross weights have higher induced drag and so require more thrust.

Now for the example. A 737-400 has a maximum gross weight of 143500 pounds and a typical operating empty weight of 77100 pounds(typical airline equipment with seats and such) giving a useful load of 66400 pounds. This weight can be split up however needed between fuel and payload depending on the length of the flight.(In practice other factors can limit gross weight such as available runway length, and payload as some engineering optimizations assume a lower landing weight than takeoff weight to save on structural weight.) At least up to the limit of installed fuel tank size, this model can hold 37708 pounds of fuel.

Some reserve of extra fuel is required for safety, diversions, holding and such, so this is usually extra fuel at landing. This is typically 4000 to 9000 pounds depending on specifics of the flight. 

Assuming flight altitude of 33000 feet and mach .74 cruise(430 knots). I am using nautical miles and short tons(2000 pounds) for all of this. 

A the most exaggerated case will be maximum range with reserve fuel of 9000 pounds.(maximum fuel at start, reduced payload) Payload will be at most 28692 pounds or 14.3 tons. Fuel burn at the start will be 6234 pounds per hour for 1.014 pounds fuel per ton-mile of payload (6234/(14.3*430), and at the end of flight 5066 pounds per hour for 0.824 pounds fuel per ton-mile of payload (5066/(14.3*430). (geometric mean of .914 pounds fuel per payload ton-mile. Change in rate is non-linear.)

If all of the useful load could be used for payload as in the case of an external fuel supply, or an infinitely short flight with no reserve fuel, you get 66400 pounds or 33.2 tons of payload. The fuel burn will still be 6234 pounds per hour but you get .437 pounds fuel per payload ton-mile. 6234÷(33.2×430)

So cruise fuel consumption with an external fuel supply will be approximately .437/.914 = 47.8% or about half of the fuel consumed per unit of cargo. Actual results will depend on variables if I must state the obvious. Longer flights would see more improvement, shorter flights less, payloads less than maximum allowable will also see less improvement, flights requiring less reserve fuel will also see less improvement.