He was sick - the whole business.

The correct word to fill in the blank is "of," completing the idiom "sick of something." This idiom means to be completely fed up with something, to be tired of it, or to find it annoying and unpleasant to the point of disgust.

In the given sentence, "He was sick of the whole business" implies that he was utterly tired or disgusted with the entire situation or activity. This is a common phrase used to express strong dissatisfaction or boredom.

Other common uses of "sick" with prepositions include:

    
• Sick with: (referring to an illness) e.g., "She was sick with the flu."
    
• Sick for: (referring to longing, less common in modern English but seen in phrases like "sick for home")

However, when expressing exasperation or extreme annoyance with a situation or an ongoing state, "sick of" is the appropriate idiomatic expression.