- ✘ The more greatly is unidiomatic.
- ✘ The less a person's eating can't logically result in them getting fatter.
- ✘ The fatter a person's eating is nonsensical in almost any context I can think of.
By the process of elimination, that leaves only one choice that is grammatical, logical, and idiomatic:
Note, however, that none of the word choices produces a sentence that is idiomatic.
In short, it should be written like this:
The more a person eats and the less they exercise daily, the fatter they are and the more likely they are to develop heart disease.
As it's currently written, it's extremely awkward and not how any native speaker would phrase it. The actual answer aside, it's a very poor example of an English question.