His back is weak because he won't try to sit up.

I could have told him there was no lump there." Colin gulped and turned his face a little to look at her.
"C-could you ?" he said pathetically.
"Yes, sir." "There!" said Mary, and she gulped too.
Colin turned on his face again and but for his long-drawn broken breaths, which were the dying down of his storm of sobbing, he lay still for a minute, though great tears streamed down his face and wet the pillow.

Actually the tears meant that a curious great relief had come to him.

Presently he turned and looked at the nurse again and strangely enough he was not like a Rajah at all as he spoke to her.
"Do you think--I could--live to grow up ?" he said.
The nurse was neither clever nor soft-hearted but she could repeat some of the London doctor's words.
"You probably will if you will do what you are told to do and not give way to your temper, and stay out a great deal in the fresh air." Colin's tantrum had passed and he was weak and worn out with crying and this perhaps made him feel gentle.

He put out his hand a little toward Mary, and I am glad to say that, her own tantrum having passed, she was softened too and met him half-way with her hand, so that it was a sort of making up.
"I'll--I'll go out with you, Mary," he said.