What is the origin of the trope where a person says "I can't eat anymore" 「もう食べられないよ…」 in their sleep? When we have scene showing a person (or many people) sleeping soundly, it's quite common to have one of them saying "I can't eat anymore" 「もう食べられないよ…」 in their sleep.

According to this forum thread on ANN, this trope has been observed in:


Cowboy Bebop (by Edward)
Air in Summer (by Kanna)
Inu-Yasha (by Shippo)
Super Milk Chan (by Milk-Chan)
CardCaptor Sakura (by Kero, also inverts the joke in one instance)
Sailor Moon (by Usagi)
Full Metal Panic? Fumoffu (by Tessa)
Gokujou Seitokai (by Randou Rino, in episode 24)


Since the forum thread above is from 2006, the examples are quite old. Below are some recent examples:


Brynhildr in the Darkness (by Kotori)


Thanks to Pawl Rowe for providing the example above

(Feel free to edit in more examples and images showing this trope, preferably from recent series).

What is the origin of this trope?
According to Chiebukuro, an early source is a 落語 (rakugo) performance act titled 「品川心中」 (Shinagawa Shinjuu, meaning "Lovers' Suicide in Shinagawa" [Shinagawa is a ward of Tokyo]) written in the Edo era (between 1603 and 1868) (unsurprisingly, the tale revolves around a double lovers' suicide). Rakugo is a form of Japanese verbal stage entertainment. A single storyteller sits in seiza position and tells a long and complicated comical story which involves dialogue of two or more characters. The art was invented by Buddhist monks in the 9th and 10th centuries to make their sermons more interesting.

Because the work was a live performance so long ago, conclusive historical evidence does not exist, but it is generally believed that the story included the following lines of dialogue:


  「ほら、あんた、起きとくれよ！」(Hora, anta, oki to kure yo!)
  
  「ふぇぇー？ もう食えねぇ～．．．」 (Fuee~? Mou kuenee~...)
  
  「何言ってんだい、お前さん、時間だよ．．．」 (Nani itten dai, omae-san, jikan da yo...)


meaning


  A: Hey, you, wake up!
  
  B: Huhhhh? I can't eat anymooore...
  
  A: What're you talking about, hey you, it's time [to get up]...


「食えねぇ」(kuenee)　and「食べない」(tabenai) both have the same meaning: "can't eat." The "kuu" pronunciation is used by men and has a rougher sound, and is also used to refer to animals consuming their food.

The inclusion of this line in various manga indicates that even to the present day, dreaming of eating so much food that you couldn't possibly eat any more is considered a good dream: such a good dream that you don't want to wake up from it.