How much of the weight of yoghurt is due to bacteria?
Interesting question and it will only be possible to do some estimation. The problem is to know the exact bacterial composition as well as the mass of the bacteria. To start, it is necessary to know the number of bacteria in a defined amount of yoghurt. There are scientific publications on this topic, but the numbers in fresh produced yoghurt are in the area of 108 bacteria per gram yoghurt and declines over time. Based on the numbers in  reference 1 and 2 I use 2x108 bacteria per gram fresh yoghurt.

The other number we need is the mass of one bacterium. This is complicated, as bacteria are very light due to their size and cannot be easily weighted. There are some numbers available (we imply here that all bacteria weight the same, which is of course not the case), and according to them, one bacterium weighs about 1x10-12 grams.

Mutiplying both numbers gives the amount of bacteria in one gram of yoghurt, around 0.0002 gram or 0.2mg. One typical sized yoghurt of 150 gram therefore contains about 30mg of bacteria. The weight of the bacteria can thus be neglected against the total weight.

References:


Survival of Yogurt Bacteria in the Human Gut
Handbook of Food and Beverage Fermentation Technology
Mass of a Bacterium