Actually, a fridge, uses EXTREMELY little energy, provided you don't keep the door open. but among the electric goods in your house, the fridge uses least of all most likely.
the amount of food in the fridge doesn't matter, as the OP sort of figured out in his original reasoning, it'll use the same amount of energy, just either take longer between using the compressor or using it shorter for more often. but even this won't matter much.
The only thing you have to check, and this has nothing to do with energy use is that you don't put hot food in the fridge. the reason for this is that it increases the temperature in the fridge, won't really affect energy use, but you shouldn't increase the temp it causes food to go bad faster and condensation. some fridges allows you to lower the temperature two r so degrees before putting in food. But this button has to be pressed well in advance of actually putting in food. (Think the day before when you know you're going to the store to buy food for the whole month). Freezers often also have this setting and allows you to press the freeze in button the day before shopping, and will lower the temperature from -18 to -22 to -24 freezing the food faster and reducing/preventing the temperature increase in the freezer.
But for anyone who wants to save energy, the Fridge, freezer and dishwasher are the least of your problem, the one thing that costs you most energy in your house, hot water. (provided you're the one providing the power to the water heater.
I just picked a random energy star rated fridge from lowes... averages 448 KW/h a year.. that's about on average $60 to run... that's an efficient one... a non energy star one now 890 KW/h.... I don't care if it "uses less then everything else in your house" it still adds up.... 500 KW/h less a year is still $60 a year I don't have to spend on electric but the reason I used this example, is because how stocked the fridge is really does not matter, it's how efficient the compressor is and how much its opened