what meaning does the watch have for Esme?

When he described the size of it on Esmé's arm, I thought it served to emphasize her fragility, that she really was a little girl, in contrast to her confident verbal demeanor. And, then when she sent it to him, this keep-sake of her father, it seemed like such a gift of trust. But, of course, it was broken, like Corporal X and many others who were in the war.