Although he is recovering from his illness, he has to follow certain diet restrictions. He cannot eat junk food.
Please do not pity him and _______________

This sentence describes someone who is recovering from an illness and must stick to strict diet restrictions. The second section warns the reader not to feel sorry for him,  suggesting that there should be no exceptions. Therefore, a phrase cautioning against loosening the rules or being lenient should be used to fill in the blank. 

The best choice in this situation is "Cut him some slack" (Option B), which means to be lenient or to go easy on someone — precisely what the speaker is advocating. When completed, the sentence would imply: Please don't feel sorry for him and relax his restrictions, which is exactly what the intended meaning is.

The other choices do not work. "Give him some snack"(Option A) is overly literal and goes against the stated dietary restrictions. The phrase "Be slack with his eating" (Option C) is poorly constructed and grammatically incorrect. "Cut down the snacks" (Option D) does not convey the warning tone of the sentence because it suggests cutting back on snacks rather than completely avoiding them or exercising self-control.

Option B is therefore the correct answer in this case.