Your Circuit looks like this to an Electronics Technician (IE: ME)
Battery--Resistor--Voltmeter and load.
As you draw current there is voltage drop across that resistor.
What is the resistor? Internal resistance in the battery.. Connections and wires all are Resistors.. A proper size wire may be only like .000001 ohm but it is still a resistor. E=IR so if you are drawing six amps (About the inverter draw with the 60 watt load) you would be looking at like 0.1 Ohm (I'm assuming yo uunplugged the fan) of total ciruit resistance. About normal.