First of all, the units were chosen to give convenient numbers. Sewage is almost entirely water, so the other ingredients are expressed as ppm, parts per million, or another unit that magnifies the numbers to avoid tiny decimals. Parts per million must have some basis such as grams per million grams, pounds per million pounds, or the like. This means that you must know the total weight and the weight of the ingredient to be tabulated. For air pollution, we switch from weight to volume, and the ppm is volume per million volume units because gases are more easily measured by volume.
Water has a density of about one gram per milliliter, and a thousand milliliters equals one liter.
It is quick and easy to measure water by volume instead of finding and using a large scale, but water can contain dissolved solids that make its specific gravity greater than one. In that case, one liter will weigh more than one thousand grams. The water in most samples of interest to the environmental engineer will be so dilute in dissolved solids that there is very little error in assuming that one liter weighs one thousand grams, but it is more accurate and rigorous to express units as weight per liter. One milligram per liter and one ppm are almost the same most of the time, but the former is the modern way of expressing a concentration. One of the analytical mainstays of environmental engineering is the BOD test for Biochemical Oxygen Demand.