Even Weikart, whose book From Darwin to Hitler: Evolutionary Ethics, Eugenics and Racism in Germany greatly overplays the connection, admits that Darwin generally tried to stay away from discussions of social, political and economic issues. In an 1869 letter to Hugo Thiel Darwin wrote "you apply to moral and social questions analogous views to those which I have used in regard to the modification of species. It did not occur to me formerly that my views could be extended to such widely different, and most important subjects". In an 1873 letter to Marx, thanking him for a copy of Das Kapital, he mentions that he was ignorant of economics.
This being said, Darwin did express some views that can be interpreted as sympathetic to social Darwinism and eugenics. There is a passage from Descent of Man (1871) oft quoted by opponents of evolution:"There is reason to believe that vaccination has preserved thousands, who from a weak constitution would formerly have succumbed to small-pox. Thus the weak members of civilised societies propagate their kind. No one who has attended to the breeding of domestic animals will doubt that this must be highly injurious to the race of man. It is surprising how soon a want of care, or care wrongly directed, leads to the degeneration of a domestic race; but excepting in the case of man himself, hardly any one is so ignorant as to allow his worst animals to breed...".
Interpretation of this passage is controversial, and Darwin goes on to write:"...but if we were intentionally to neglect the weak and helpless, it could only be for a contingent benefit, with an overwhelming present evil. Hence we must bear without complaining the undoubtedly bad effects of the weak surviving and propagating their kind; but there appears to be at least one check in steady action, namely the weaker and inferior members of society not marrying so freely as the sound; and this check might be indefinitely increased, though this is more to be hoped for than expected". See Wikiquote for the full context and discussion.
Weikart also makes much of 1872 letter that reads "I fear that Cooperative Societies, which many look at as the main hope for the future, likewise exclude competition. This seems to me a great evil for the future progress of mankind. Nevertheless under any system, temperate and rugal workmen will have an advantage and leave more offspring than the drunken and reckless." See Recently Discovered Darwin Letter on Social Darwinism for the full text.
The bottom line is that Darwin was not particularly interested in these issues, but he did make passing comments that look offensive today.