It really depends on how the shelf is mounted to your wall. If you're into numbers, you can use the formula:
$$\text{Load Capacity = (Material Strength × Width × Thickness × Thickness) / (8 × Length)}$$
But I suppose material strength values aren't that easily available, and specific shelfs can be more complicated, so you'll have to resort to experimental tests.
An aquarium is a stationary load. If your shelf can hold it for a few seconds without bending, it can hold it for an indefinite period of time (hopefully). So I suggest you just keep the aquarium on top of it and be ready to hold it if the shelf falls. Testing with smaller loads will only prove that the shelf can handle those smaller loads; the behaviour is unpredictable for larger loads as shelf-failure is an abrupt event with no observable signs beforehand.
Better to just go off of your intuition and install additional supports if required.
very small
is not a unit of measurement ... to some people, a very small aquarium is anything smaller than 500 liters $\endgroup$very small
is not a unit of measurement. My hope is that there may be a way to calculate or more likely test the sturdiness of the shelf in a way that does not cause permanent damage. If I know how many pounds it can handle I can correspond that to how much an aquarium would weigh. Bags of flour/sugar sounds like a potential situation. Could I also add water slowly and see if it bends? Or could it crash down all at once—no bending required? Thank you all so much. $\endgroup$