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 _______________

'Cut someone some slack' means to go easy on someone or relax the rules for them. The speaker asks the listener neither to pity him nor to relax his diet, since he must keep to his restrictions. 'Give him some snack' is ungrammatical, and 'be slack with his eating' and 'cut down the snacks' are not idioms and do not fit the request not to pity him.