First, this person is identified as a 'nurse', but that doesn't necessarily mean she actually is an RN or LPN. A lot of the people who work in doctor's offices identifiy themselves as "Dr. X's nurse" when they are medical assistants. The reason for mentioning that is the person may not have as much training as a nurse would have in how to approach people. And, whatever training she had, she might have been told not to say people's weight out loud.
Second, it's possible that she used the calculator to show the weight because she needed the calculator to convert the weight from kilograms to pounds. That makes a lot of sense and was probably why she had the calculator with her.
I think she could have done a little better job of her first statement - like "I need to convert it from kilograms to pounds. Let me figure it out on the calculator and I'll show you." Or, if she didn't have to calculate it, just say "A lot of people don't want their weight said out loud, no matter what they weigh. Here, let me show you on the calculator."
It's also possible that she normally tells the weight back in the room after plotting it on the growth graph. So, your DD asking about it before that point may have thrown her for a loop.
And, finally, I think your DD gasping had nothing to do with how she was told her weight. I think she would have reacted the same way if the nurse had just said, "You weigh 118 pounds." In a world where 14 year olds know that Lindsay Lohan is a size 2 and Mary Kate and Ashley Olsen are size 0, that 118 pounds sounds huge to them, no matter how they are told.