"Dika" means "thick", but is interpreted in this context to mean "fat". Kinda like how "necesejo" literally means "necessary place", ha know? In many places in America, we likewise understand the word "thick" in this context to mean "fat" -- to indicate "stupid", we say "dense".
Well, you decide it learning about the meaning and value of each Esperanto preposition. In this case, "por" conveys the idea of purpose, goal: for that purpose, he is too fat. The Romance languages use the equivalent form of "por" (pour, per, para, etc.) in this kind of constructions: Está demasiado gordo para correr ES, Il est trop gros pour courir Fr, Lui è troppo grosso per correre. The "problem" with English is that you "mix up", so to speak, the value of "to" as a proper preposition and its value as a marker for the infinitive (the to-form), so in sentences like these you feel that there is no preposition, but there actually is: "to", with the meaning of "in order to".