The weight difference is due to residual propellants in the engine. The engine cannot run dry, mainly for two reasons.
The first reason is the bearings in the turbopumps. They need to be constantly cooled by the pumped fluid. Because this is a LOX-Kerosene Engine, the cooling is done with Kerosene, as can be seen on page 11 (p.25 of the pdf) of this document:
The barrier seal is clearly marked and located on the oxygen side of the bearings. In Kerosene, an overheating bearing can cause all sorts of headaches, such as thermal stress and as a result little spalls that could cog something downstream.
In hydrogen-oxygen engines on the other hand, the oxygen and hydrogen pumps are on separate shafts, because the lower density of hydrogen means that a higher rotational speed is needed. In that case the LOx pump bearings are cooled by liquid oxygen and running them dry is disastrous. The pump will ignite very quickly. This happened on a test stand for the SSME bearings once. Notice the scary font on page 25 of this pdf:
The second big reason that comes to my mind is the regenerative cooling. Whatever propellants and pressure you use, the combustion temperature is by far larger than the survivable temperature of your chamber wall. In the F1, the chamber is cooled by the fuel and the nozzle extension is cooled by a film of dumped turbine exhaust.
When the engine is shut down by closing valves directly downstream of the pumps, the fuel is left stagnant in the cooling tubes because there is nothing to push it onwards.
It is possible to purge the channels using an inert gas, but then the tubes would be filled with gas, while the engine still burns, possibly causing an unclean shutdown. Probably not an explosion, since the cooling channels are filled with inert gas now, so them burning through will not be so much of a problem. However, the additional complexity is most likely not worth it, especially for a first stage.
As for the nozzle extension, the cooling requirement is not quite as high here, and it is cooled by gas to begin with. When the main valves close, the gas generator is quickly drained of propellants and the cooling of the nozzle extension stops. But since the combustion chamber is extinguished a the same time, this is not likely to cause any trouble.