べちゃった　＝　食べてしまった ～てしまう　＝　to do something completely. There is a hint of "Oh no!" at the end of some of these sentences. In this case, it appears she ate too much.

it may help you. http://www.youtube.com/watch?v=QWEZQQyRPv4&feature=my_liked_videos&list=LLELvPOyh8l2HUVjUohY62sQ

食べちゃった is a colloquial/collapsed form of 食べてしまった。 食べてしまった would be more like "I've eaten", while 食べた is "I ate", the simple past tense. 食べました is the polite version of 食べた, and the polite version of 食べてしまった is 食べてしまいました, and that of 食べちゃった is 食べちゃいました. 食べちゃった/食べてしまった etc. can be used to express "completion", but here it shows that the speaker has eaten a lot and that she regrets that now.