Given identical insulating values in construction and identical thermal mass values for the materials used for construction, larger kilns use less energy per contained cubic foot/meter than smaller kilns do. Additionally, as a percentage of the total FIRED LOAD WEIGHT, a larger periodic kiln will also use less energy per pound of fired output to that used to heat the kiln structure itself.
One factror here is the surface area to volume relationship, since a large amount of heat loss is thru the surface of the kiln. Ignoring wall thickness for the moment, if you have a cubic kiln that is 1 foot on a side exterior dimension, the surface area is 1 square foot per side, and there are 6 sides...... so 6 square feet of total surface area. If that kiln is doubled in linear size to 2 feet on a side (which changes the interior volume to 8 cubic feet), we then have six sides that are each (2x2) 4 square feet of surface, for a total of 24 square feet of surface area. If we again go to a 3 foot cube, the surface area becomes six sides with an surface of 9 square feet for a total surface area of 54 square feet, in which the volume increased to 27 cubic feet. The ratio of the volume to surface area on the 1 foot cube is 1 to 6. The ratio of the volume of the 2 foot cube is 8 to 24....or 1 to 3. The ratio of the volume of the 3 foot cube is 27 to 54....or 1 to 2. See what is happening? As that ratio gets smaller, the amount of contained volume relative to the surface area gets larger.
(Plotting basic function y=aXb.......... Surface Area = 6 x2 where x is the linear side length of a cube)
But in a fuel fired kiln, the largest percentage of the heat losses by far is with the by-products of combustion that must be vented from the chamber. So the relationship of surface area to heat loss is not really fully linear.
In general, bigger kilns are more efficient (energy wise) than smaller kilns. Better to fire one 100 cubic foot load then two 50 cubic foot loads if you are looking solely at energy usage issues.
The amount of energy to fire a load in a given kiln depends extensively on the efficieincy of the heat transfer from the heat source to the load. Secondarily but importantly it also depends on the mass of wares that are being fired. To fire 100 pounds of clay+glaze to a given heat work level will take the application of twice as much heat energy as it would to fire the same clay+glaze materials in a 50 pound load. This relates to the LOAD of ware only.
You do have to account for the thermal transfer impacts of a partially loaded (less dense) packing in a kiln also. Depending on the kiln type this can caues either MORE efficient transfer of heat energy or less efficient transfer of energy. So the "double the energy for twice the weight" is a tad affected by this factor. But it is a very small percentage affecting this number.