Question about arimasu and desu

Hiii everyone!
So i have this little problem, i know than "arimasu/imasu" is about the existence of a thing and "Desu" about how is it that thing.
So why the phrase "I'm fat" is translated like "私は太っています" instead of "私は太ってです" if i am talking how i am and not about existence?
Because "i'm a student" is translated like "私は学生です" why "I'm fat" doesnt use desu?

Thanks in advance ^!