Saying something reassuring when you (or someone else) sneezes is an old Jewish custom, though of course other people do it too.
A famous midrash on Parashat Vayechi says that Jacob was the first person to become sick before he died. Previously people would sneeze and immediately expire.
The Torah Temima (Rabbi Baruch Epstein, 1860-1941) refers to Rashi's comment on the Talmud that you say "asuta", "May you be healed", when someone sneezes. According to the midrashic collection Yalkut Shimoni, someone who sneezes must thank God. Some people, Rabbi Epstein writes, say "God, I await your salvation" when they sneeze. He adds that although it is only a minhag for others to say l'chaim u'lshalom ("to life and peace") when someone sneezes, it should be a rule that the sneezer say some words of gratitude to God and he doesn't understand why most people do not. Perhaps it is because, thank God, sneezing is no longer a sign of mortal illness.