The ‘bless you’ response to a sneeze was enacted by one of the popes during the bubonic plague. So it definitely has a non-Jewish whiff about it.
But long before that, Jews blessed each other upon sneezing. The Talmud records that in the earlier generations, people didn’t get sick before they died. They simply sneezed and their souls left their bodies. So it was customary to wish a sneezer “To Life!” for fear that their sneeze was a herald of death.
Things changed in the times of our forefather Jacob. He prayed that one should rather get sick some time before dying, in order to have a little warning and time to prepare for leaving this world. His request was granted, and so sneezing alone was no longer a sure sign of impending death. But it still could be a symptom of illness, so the custom arose to wish a sneezer good health – Assuta in Aramaic, Tzu gezunt in Yiddish, or Labriyut in Hebrew.
Interestingly, one source says that after being blessed with health, the sneezer himself should respond to the one who blessed him “Bless you!” (Baruch tihyeh in Hebrew). Another interesting note: the sages taught that one does not respond to a sneeze while in the middle of studying Torah. Torah study is too holy to be interrupted, and anyway its power will protect the sneezer from harm.
Indeed these days most people survive a sneeze without any major consequences. But that doesn’t mean we should no longer wish each other good health. Words have power. The more we bless each other the better. A sneeze is as good an excuse as any to bless someone.
Mendel (Menachem) Bluming
Talmud Bava Metzia 87a, Brochos 24b
Pirke D’Rebbi Eliezer 52
Shulchan Aruch Yoreh Deah 241:17 etc