Keep in mind that our doggies are very much in tune with our feelings. Colby might be sensing your anxiety about him eating. He might associate your anxiousness with something negative about his "dog" food (along with his knowledge that if he holds out long enough, he will get the "people" food).
Maybe I was lucky getting 2 good, non-picky eaters, but I do believe a really positive attitude toward their food helped. When I feed my boys, I behave like their kibble (sometimes with fresh steamed chicken) is solid gold on a plate.
We are almost this goofy:
https://www.youtube.com/watch?v=tYnQQL5oB7k
When they finish eating, they come to me and I have to rub their shoulders while saying, "Mmmm, that's good stuff, isn't it?"
We also use their kibble for potty rewards and trick training.
Admittedly, Max's first year, I had to hand feed him. He chose to perform sits for each kibble. I sped up the process by devising a game of "kibble in the Kong," putting a bunch of the kibble in the Kong toy and singing a little song. Adding a second Yorkie encouraged Max to eat on his own.
You might try getting samples of other foods to see if it is a taste thing, but try to mask your concerns and make meal time fun.
If Colby is vomiting bile from not eating, I would give in and feed a little fresh chicken, or something that is close to the food you want him to eat.