Oh, I was thinking that he was always sickly, but that's kind of why Giovanni's worried about the possibility of him turning. Of course, no ones actually turned yet, so they don't actually know about the monsters, but once they start showing up, he'll begin to worry again. Also, I'm thinking that the plague works by killing most, and then turning most of the rest, so even if you're immune to the properties that kill people, you aren't necessarily immune to the transformative properties.