An engine needs fuel to keep itself running.
There is a lot of heat rejected from the radiator and exhaust.
You have to burn fuel to produce that heat.
A loaded diesel gen-set will produce about 13 Kilo Watt Hours per gallon of standard diesel fuel.
As the load drops the ratio of load to losses drops and the efficiency drops.
We had to run our home on a small diesel set (6 KW) for a couple of months.
During the night it had to be kept on line for two reasons.
1. Power had to be available for the freezer, refrigerator, furnace and sewage pump out.
Most of the night the set ran unloaded.
2. Did I mention that the ambient was -20F to -30F.
Power had to be available for the fan in the natural gas furnace, and with no other power, if the set was left cold all night there would be no starting in the morning.
By far the most fuel consumption was during unloaded hours.
If your set is for occasional standby this may not be important.
If the set will be used frequently, fuel consumption becomes more important.
Another issue with low loading is wet stacking.
Modern diesel engines use the combustion pressure, ported to the back of the compression ring to help seal the rings.
At low load, there may not be enough combustion pressure to properly seal the rings and oil pumping or wet stacking may result.
The next step is the possibility of flaming globs of oil being expelled from the exhaust.
The other result is loss of lubricating oil.
Worst case, A new set, was started and left running with very little load a few days after I installed it.
In a few hours it pumped out all of the lube oil and shut down on low oil pressure.
Avoid a diesel set that is much oversized.
In cold weather, a radiator shutter or baffle to reduce the heat rejected from the radiator will improve fuel economy.