In a gesture of politeness by offering her a coat since she was clearly not dressed for winter, Nabooru thought that Byrne was implying she was weak? He was about to berate her for that, but then he realized that if he had been in her position, he would have thought the exact same thing. He didn't need help or charity or any of that.

"No..." he said, "No, you don't seem weak."

She wasn't as strong as him, of course, but she wasn't a person he would label as "weak." Physically, and even mentally too. Her resolve to go through with her Sagedom was not weak, even if it was a bit moronic.

Her confidence and strength was something he admired about her, and if she had been an annoying weakling, perhaps he wouldn't have stuck around for so long.