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Any teenager will be hyper sensitive even to what they feel is the slightest criticism (although you're actually trying to help her by motivating her)
She most certainly knows that you mean well. Since you know her better than anyone else, think of some times when you gave her feedback in a neutral way as to where she did not feel afflicted.
Perhaps stocking the fridge with healthy things and encouraging her to eat those versus what teens ofter chose (junk food and sodas), getting some exercise DVDs and when you exercise with her next time let her know that those are also available in case she wants to exercise by herself.
There are different bathing suites that can compliment a figure and finding a bathing suite in which she would feel comfortable can make her feel good.
Just be weary of any unhealthy eating habits on her such as binging or purging or restricting food intake or of overexercising (since those can lead to eating disorders and these are common in teens and young adults)