
I think its a mixture of both. Waki cant stomach other kinds of food cuz it reminds him of Kami which in turn is leading to him having poor health. Hence the fasting. Waki cant do his job which is him eating food with a smile. Why would he force himself to fast in an attempt try get Kami back even though he know Kami made his decision to leave? Waki previously stated he wanted to send Kami off with a "smile."
Lets all agree that they are both doing terrible and need to get over whatever it is that is basically killing them.

True. I guess some just don't look deeper into the story. What was that old saying? hmm *thinking* "look beyond what you see? or read between the lines?"
Yea I think it was the second one. Anyway, we won't know how it will end until the next chapters get translated and released. Hopefully, we find out the truth and get a Happy End (which most likely will happen).
Waki was probably tasting all kinds of food when Kami was gone, hoping that at the very least, he can still convince himself that he can eat and properly taste food cooked by other people (to continue his show like what Kami wished for him). The food binge caused Waki to gain weight and now he needs to fast (╥﹏╥)