The idea that those with mental and physical handicaps are a burden on society falls right in line with this thought process. Handicapped people, babies born with deformities, sickly people, etc. only exist to hold back the superior human beings who are able to contribute to a better more productive society. Galton's statement just makes sense when you understand what he believes. He believes in survival of fittest, which is built from an evolutionary foundation on the origin of mankind. Many evolutionists would argue that our actions must be a reflection of what's best to not impede progress in the evolution process. Not all hold this view, but those who are considered to be evolutionists with no belief in a higher power often do. .
So, aborting a child that would be born with birth defects would be acceptable, aborting a child in order to limit population growth would be acceptable; aborting a child that someone doesn't want and would only become a burden to tax payers would be acceptable. This would also apply to the elderly. Those of advancing years who draw social security and Medicare benefits for many years and are a huge drain on the medical supply could be argued as an unnecessary burden on society. In other words, the value of someone's life is measured on a scale of productivity, contribution, and whether or not that life impedes others. Without high output in these areas, the value in that life is not there. .
This mindset also believes that some "races" of people are less evolved than others and of less worth. In the book, "The Lie"," Ken Ham gives an example of this, "Hitler believed in struggle as a Darwinian principle of human life that forced every people to try to dominate all others; without struggle they would rot and perish Even in his own defeat in April 1945, Hitler expressed his faith in the survival of the stronger and declared the Slavic peoples to have proven themselves the stronger.