Are these cockatiels? Your poor guy is molting at a bad time since he is trying to care for a hen and eggs. She would normally groom the feathers on his head but she is occupied with the eggs. Breeding birds should not be disturbed at all, so it is unusual that he is wanting you to handle him. Hopefully this is all due to the molt. Since they do have eggs, they need a lot of nutrition. If you are only offering seeds, this is one reason why he is having a hard time with the molt. Your birds need a nutritionally balanced diet, including chopped veggies and fruits and dark leafy greens. Since they have eggs, you can also offer multi grain bread and cooked eggs, with the shells broken and cooked with them. Both birds need extra nutrition and the female needs to be getting enough calcium. If you are concerned that he is sick, then you need to take him to an avian vet. Otherwise, make sure they are getting enough nutritious foods and give him time to get through the molt.
Here is a link to our feeding guide:
Bird Food Guide
Thank you for asking Lafeber,