So, I call my kids "Fatty" and "Lil' Chubs"...
Ok, well not in those terms exactly, or even in that language to be exact.
I call my daughter "Gorda" or "Gordita" (Spanish for fat and its diminutive form) and I call my son "Gordo" or "Gordito."
The translation into English sounds terrible, I know. In my defense, it is not my fault... it's cultural... well, not my culture, or not my 1st culture anyway, my 2nd culture: Chile.
Terms of endearment in Chile, (and most of the Spanish-speaking world, but I will refer to Chile, specifically, since that is what I know best) are not "sweet" as they are in the U.S. They don't call their wives/husbands, sons/daughters "honey," "sweetheart," "pumpkin," or "sugar."
They call them "gordo" and "gorda." There are a few alternatives every once in a while: "flaca/flaco" (skinny); "negro/negra" (black); and "guaton" (big-belly). These are actually nicknames your classmates and friends might have for you at school as well, but are genearally not mean-spirited.
Calling someone "gordo/gorda" or "flaco/flaca" is not an insult and it doesn't necessarily have to do with actual body size... I mean, it might, conincidentally, but that is just what they call everybody.
I didn't really want to use these terms with my kids, especially my daughter, since we are, for now, living in the U.S. and weight is such a sensitive issue here, not the matter-of-fact characteristic it is in Spanish-speaking cultures. But that is what my husband calls her and what his family calls her... and it is contagious, and it just sticks... and once I started calling her that, I can't stop. With my son it went down the same way. So what can I do?
I have many other terms of endearment for them too, in both English and Spanish, and this is just one of them. (I hope they never feel bad about it.)
My husband does not call me "gorda." I think I insinuated early on that it would not sound particularly endearing to me. So he calls me "piojito" which means "little louse"... but in a totally sweet and loving way.
You can read more of my sins here, here, and here.