There is an interesting article here, on the evolution of the moniker.
I think it also comes about through the use of a couple of slang terms of the time.
Big Cheese: Either meant someone who was powerful (The leader of a gang or the police chief) It was also used in a sarcastic way to describe someone who thought they were a big shot, but weren’t. (Adding the “Red” made sense since his costume is pretty much all red)
Big Red Cheesecake: Cheesecake was a term for pinup models popular in that time. I think Sivana’s use of it was a way to refer to “that guy thinks he’s a big shot but he’s really just a “woman”, all muscles on the outside but not a “man” on the inside. To be brutal, the term cheesecake could equate a term I am loathe to even use, however, it has been used for quite some time and unfortunately still is, the term “fa@@ot”, used as a general pejorative about a male. Especially as an attack to the “masculine nature”.
It’s quite a sad commentary to think that Sivana basically was calling Captain Marvel an “egotistical nobody f****t”. But, if you break down the sociolinguistics of the time, that’s basically what he’s calling him.
The Big Red Cheese, (not cheesecake, because that probably wasn’t going to make it past the editors more than a couple of times) becomes a label able to be used either way. Used by Sivana, it is an insult, because it is used sarcastically. By the fan base it’s a positive because CM is “the big cheese” (powerful, big shot) of superheroes.
I just realized as I was writing this. Sivana is the one villain in the DCU that I have always wanted somebody to really kick the snot of him. Full body cast required, kick the snot out of. Have Sivana say the wrong thing to Guy Gardner or even better, the JL/JLU Hawkgirl and watch him just get pummeled into darn near paste. And I think it’s because of his use of language. Especially the cheesecake remark.