What is the healthy weight for a 5 foot 10 14 year old girl?

Optimal weight. For a 14 year old girl at 5'10" should be between 110-121 pounds.
Agree w Dr. Lurie. 110 to 120 lbs is super-model thin, and both unrealistic and possibly unhealthy for most 70 inch girls. While thin is healthy, a 14 year old trying to achieve that sort of rail-thin body, unless she's naturally extremely thin, is possibly harmful and a route to developing an eating disorder. At 110 lbs and 70 inches, the bmi is 15.8, which fits some definitions of anorexia nervosa.
There's a range. Depending on the bone structure of the girl, the average healthy weight would be around 160 pounds. That correlates with a bmi of around 23. The normal bmi is between 19 and 25 which would mean the range of normal weights is between 136 and 172. You can figure out the bmi with the bmi calculator online by plugging in your height and weight.