Is the stove a gravity fed design? If so, is the tank vented in any way? If not, it could be air trying to get into the tank... which would happen more with a full tank, since the air space is smaller and it takes less time for the vacuum to build to the point it'd need to draw air into the tank. If the tank is vented, check the vent line for a clog.
A GRAVITY FED kerosene stove???
Never heard of such a beast. All kero stoves I know are pressurized.
And yes, the tank is close to the burner. In a well-designed stove the tank gets warmed up by the burners so usually you don't have to pump it up again during use. If there is a need for manual pumping, I take it as a sign that I have to refill the tank.