When those who labour for their daily bread have the misfortune to catch cold, they cannot afford to lose a day or two, in order to keep themselves warm, and take a little medicine; by which means the disorder is often so aggravated as to confine them for a long time, or even to render them ever after unable to sustain hard labour. But even such of the labouring poor as can afford to take care of themselves, are often too hardy to do it; they affect to despise colds, and as long as they can crawl about, scorn to be confined by what they call a common cold. Hence it is, that colds destroy such numbers of mankind. Like an enemy despised, they gather strength from delay, till at length they become invincible.--From Domestic Medicine--
Now I understand the phrase: "that which does not kill you, only makes you stronger." It's about colds. If you spread them to others and they die you have less competition.
[Note that the author isn't talking about the disease spreading to uninfected people from infected people who refuse to isolate themselves. That idea isn't mentioned in this medical treatise.]