Fatsy is a term when describing someone of upper rank, or superiority in actions. Like, clothes or demeanor. When saying some one is fatsy you are telling them that they are nicely put together in a very superb way.
"Wow, he is so fatsy!" When seeing a delicious man in a tux with very wonderful hair, and air.
"I wish I were as fatsy as her..." When addressing a woman who is obviously much better put together than you.