The Moctezuma who eventually lost to Cortes was the nephew of a much more powerful king who died of smallpox. And the death of that great king encouraged some of the smaller states in the Aztec Empire to rebel, and some of them even fought for the Spaniards. And another side effect of disease was starvation, because there simply weren't enough people left to grow crops to feed the living. And then malnutrition made survivors that much more susceptible to disease. In short, it sucked. The transmission of disease largely went one way, from the old world to the new, but the Americans did have one gift for Europe, venereal syphilis. It showed up in Europe around 1493, and even though Europeans are very fond of ascribing syphilis to each other, Italians called it the French disease, the French called it the disease of Naples, Poles called it the German disease, Russians called it the Polish disease, the truth is venereal syphilis was spread by sailors who'd returned from the Americas.