If you do something huffily, you do it in a small, offended bad mood. Someone has hurt your pride, and it shows in your voice or your body. A person who answers huffily is not shouting with big anger; they are sulking a little, as if to say “well, fine then.” Short replies, a turned shoulder, a door closed a bit too hard — that is the picture. It is informal. It comes from huffy plus -ly, so it tells you how the action was done, not what kind of person someone always is.