My son, who also has food allergies (hazelnut, peanut, garbanzo bean) lost weight between his 17 and 18 year check up. He was always on the thin side and would stop eating when he was full. Even things he loves. He does eat chicken, pork, steak, fruit, and fish so slightly different situation. He started drinking strawberry and cream premiere protein shakes with breakfast every morning. He is off at college so he handles his own food. We did discuss that he needed to gain some weight and he did gain about 9 pounds this year. The shakes were key for us. They are safe for him with his allergies, and they do not have to be refrigerated until opened and are easy to grab. He does prefer them to be cold though. He also eats Madegood breakfast bars and apple sauce squeezers in the morning for breakfast. Oh, and a cup of coffee from his keurig. Perhaps buy a few of these shakes for him to try. They sell a mixed pack on Amazon. We bought the assortment and he tried them and decided strawberry and cream are his favorite.
https://www.target.com/p/premier-protein-nutritional-shake-strawberries-cream/-/A-94461875?preselect=50835895#lnk=sametab
Best of luck!