Thin puppies are better than fat puppies IMO, but upping his fat intake is a good start if he's just needing to gain weight. I add a small amount of oil (coconut or fish) or a bit of a fatty cut of meat if the dog needs to get heavier.
I do agree with not catering to a healthy, picky puppy. I made the mistake of doing that many years ago because I thought my Papillon was ever so slightly too thin, and he was a nightmare to feed even into neutered adulthood. All the dogs I've raised since then existed on a "don't like it, don't eat it" policy in which the bowl is on the ground for about ten minutes, and if they ignore it any longer, it gets picked up.
All my dogs since then have been happy to fatten up, especially the skinny Mexidogs. Cricket had to learn about eating in a timely manner as a young one, because she'd play with her raw meals instead of eating them and then cry when I took them away lol.