I've taken the time out of my life to pore over this scholarly work, and I provide to you, at literally no charge, the hidden meanings behind the whole novel.
1. Christian Salvation
The Caterpillar represents one of us human beings, specifically, a non-Christian human being. He spends Monday through Friday indulging in the fruits of sin, Saturday indulging in guilt pleasures, which cause him to be ill (The conscience enacting its Catholic revenge on our tubular friend) before finally, on Sunday, he tastes the leaf of salvation, is cured of his guilt, and metamorphoses into the angelic being that is the butterfly, shedding his pointless, furry body. Obviously, this is just one interpretation.
2. Russia under Communism
The regimented structure of the Caterpillar's diet clearly represents the brutal totalitarianism and dictator structure under Stalin, whilst the Saturday spent experimenting with different foodstuffs (Outside of the expected fruits, but not specifically a leaf) represents the transitional period, when Soviet rule was relaxed and many young Russians enjoyed a freedom they had not had in the past, and experimented with new things. Then, Russia, finally, takes the leaf of capitalism, and transforms from a seemingly backwards communist nation into the angelic butterfly that dominates the map today. Remarkably prescient of the author, given that the book was written in 1969, and the USSR didn't collapse until 2 decades later, but all we can assume is that authors of children's books know more about global politics than we think. JK Rowling certainly keeps warning her closest allies about the danger Iran poses to the modern west (Not true).
Just two examples of the hidden depths to this much-loved children's classic, that you may never have known about. I advise you to peruse it at your leisure and see how hungry that caterpillar is. Hungry for salvation? Hungry for capitalism? It's hard to say, all I can do is point out the connections.