If you have had a bellyful of someone or something, you are tired of them. You have had to deal with them for too long, and you do not want any more. People almost always say it in this shape: “I've had a bellyful of…” — not the word standing alone, and not “I am bellyful.” It is informal. You hear it more from British speakers than American ones, and a little more from older speakers, though it is still alive. The picture is your belly: you have “eaten” so much of this trouble that you cannot take another bite. Nobody is talking about food. You can have a bellyful of a person, of excuses, of noise, of waiting. It is stronger than “I've had enough”; it has a fed-up, slightly blunt feel.