Are you just asking about the weight requirements of competitive gymnastics? Because there's a lot more to gymnastics than weight and diet. Gymnasts workout several hours a day and need to eat healthy food to make it through those workouts. Obviously weight is important, but eating sensibly and doing gymnastics workouts should be enough for most gymnasts.
Gymnasts must also be fully dedicted to their sport. Getting enough sleep is important. Dealing with injuries is important and learning to work though some aches and pains is crucial. There's also dedication to a conditioning program and the mental strength and preparation to deal with fear and perform well in meets.
I joined an elite gymnastics school when I was 13. The first thing I was told was "Interest means doing gymnastics if possible. Dedication means doing gymnastics no matter what, and dedication equals winning."
I love that quote. Except I kinda feel bad because I left the school after six weeks....
You need to be dedicated, that is the main requirement. Competitive gymnastics requires at least 3 days a week of training more often 4, 5 or 6 days a week and training usually last 3-4 hours each day. This is year round, usually you will get around 2 weeks break throughout the entire year. So basically dedication and committment is the biggest requirement.