In "it seemed somehow to be a sort of slight", the word "slight" means

I remember going to the British Museum one day to read up the treatment for some slight ailment of which I had a touch—hay fever, I fancy it was. I got down the book, and read all I came to read; and then, in an unthinking moment, I idly turned the leaves, and began to indolently study diseases, generally. I forget which was the first distemper I plunged into—some fearful, devastating scourge, I know—and, before I had glanced half down the list of “premonitory symptoms,” it was borne in upon me that I had fairly got it.

I sat for awhile, frozen with horror; and then, in the listlessness of despair, I again turned over the pages. I came to typhoid fever—read the symptoms—discovered that I had typhoid fever, must have had it for months without knowing it—wondered what else I had got; turned up St. Vitus’s Dance—found, as I expected, that I had that too,—began to get interested in my case, and determined to sift it to the bottom, and so started alphabetically. I plodded conscientiously through the twenty-six letters, and the only malady I could conclude I had not got was housemaid’s knee.

I felt rather hurt about this at first; it seemed somehow to be a sort of slight. Why hadn’t I got housemaid’s knee? Why this invidious reservation?

I sat and pondered. I thought what an interesting case I must be from a medical point of view, what an acquisition I should be to a class! Students would have no need to “walk the hospitals,” if they had me. I was a hospital in myself. All they need do would be to walk round me, and, after that, take their diploma.