When you are a guest at someone’s house you do not, repeat do not, set down your plate/cup completely empty. A few bites/sips are left in the plate/cup to show that you are shab3an or “full.” Setting them down empty, on the other hand, is a sign that you’re in need, and hence aren’t “full.”
I’m still not quite sure what “full” means, but I’m pretty sure they don’t mean full stomach-wise. More along the lines of you’re used to wealth, you’re used to having your needs fulfilled. Ergo you’re not going to pull out your evil eye and blast them with it.