In this passage, we are presented with a description of Sherlock Holmes injecting himself with a syringe. Watson, who is disapproving, asks the detective which drug he is using -- morphine or cocaine? Holmes answers that it is a seven percent solution of cocaine.
This is probably the most famous account of drug use in all of the Sherlock Holmes stories. It establishes that Holmes has what Watson would characterize as a drug problem. But does the account show Holmes to be an eccentric?
If we consider only the description of drug use, we might argue that Holmes isn't being portrayed as particularly eccentric. In 1890, when the novel was published, cocaine and morphine were in wide use. The drugs were prescribed by doctors for a number of ailments, and used by many conventional, middle class people. Moreover, even if Holmes's drug use is excessive, that doesn't make him eccentric. Addiction and drug abuse weren't uncommon.
What's more telling is the language Conan Doyle uses to describe Holmes' manner and Watson's sense of intimidation. Watson says he has seen Holmes inject himself three times a day for months, and he has disapproved. But he never spoke up because "…the cool, nonchalant air of my companion which made him the last man with whom one would care to take anything approaching to a liberty."
Watson says he rebuked himself nightly for lacking the courage to protest, and when he finally does speak up, it's a very weak protest indeed. He merely asks which drug Holmes is using, and then refuses Holmes's offer to take some cocaine himself -- with an explanation that seems designed to avoid further confrontation:
"No, indeed," I answered, brusquely. "My constitution has not got over the Afghan campaign yet. I cannot afford to throw any extra strain upon it."
Is Holmes aware of the effect he has on his friend? That seems evident, and not just from his prior reputation as an excellent reader of human emotional reactions. The language in this passage suggests that Watson's emotions were clearly on display. Watson says "from day to day I had become more irritable at the sight" of Holmes engaged in drug use. He speaks of his "…additional exasperation produced by the extreme deliberation of [Holmes's] manner."
In this context, the true nature of Holmes's eccentricity is revealed. He is surely aware of Watson's feelings, yet he openly, and with "extreme deliberation," uses drugs in front of him. He senses the disapproval in Watson's question, but offers no acknowledgement of it. Instead, he asks casually if Watson "would care to try" the seven percent solution himself.
Thus, it isn't so much Holmes's drug use that makes him appear eccentric, but the show of indifference he makes to his friend's discomfort, and the qualities that inspire Watson to back down.