First, there is really no such thing as human races. It is far more accurate and appropriate to talk about the UN sanctioned ethnic groups. There are well over 5000 and some would say closer to 7000 such groups in the world today. Each group as traits that make it distinct some are minor others are obvious. There is no worth attached to it, just a manner of classification.
But, for the sake of the discussion I will use the 4 historically most common 'race' groups when talking about their breasts. Much of this came from my research a few years back into what really was a "large" chest. Finding what was common or average and why it was helped to set a baseline. Please note that even these base four 'races' have not had consensus and yes, I am including the Australian aboriginal groups. I will call them Cs, Ne, As, Ab.
If you were to average ALL the boobs of the world and gave the physical characteristics of this non-existent omni-boob a base factor of 1.0 this is how a core representatives of each 'race' would stack up in terms of breast softness.
Cs = .95 to 1.20
Ne = .95 to 1.25
As = .80 to .95
Ab = .90 to 1.05
The lower the number the more dense the breast. Basically breasts range from around .8 to 1.25 give or take .05, so about 20-25% more or less dense from the average.
Again I want to stop here and say that there are a multitude of factors that effect sizes and no one person is genetically exactly 100% of a 'race'. This is especially true of areas with generations of humans intermingling, conquest or migration - which is most of the planet.
But if you have a genetic propensity for dense breasts it takes much more "big breast" factors to generate a large looking (volumetric) boob. That is why the 'As' group with the propensity for high density will tend toward smaller sizes.
Yes, other factors such as diet, weight, social pressures, mate selection, etc. also have influence. But an aspect with strong correlation and consistent research findings would be breast density.
Also - the stereotypical 'As' only exists as a concept. The 'As' group is highly diverse like any of the basic groups and it is obvious that one individual can express traits to various degrees. Due to genetic mixing it is very likely that any one person, even from a traditional stereotypical region (say Japan) could express exceptions to the common physique.
I find the long outdated and blunt concepts of races too general to make for any manner of classification due to the wide variety within each 'race'.
Show me your haplogroup and I will show you mine.