Old English cancer "spreading sore, malignant tumor" (also canceradl), from Latin cancer "a crab," later, "malignant tumor," from Greek karkinos, which, like the Modern English word, has three meanings: a crab, a tumor, and the zodiac constellation represented by a crab, from PIE *karkro-, reduplicated form of root *kar- "hard."
Greek physicians Hippocrates and Galen, among others, noted similarity of crabs to some tumors with swollen veins. The Old English word was displaced by French-influenced doublet canker but was reintroduced in the modern medical sense c. 1600. In reference to the zodiac sign from late Old English; meaning "person born under the zodiac sign of Cancer" is from 1894. The sun being in Cancer at the summer solstice, the constellation had association in Latin writers with the south and with summer heat. Cancer stick "cigarette" is from 1959.