My son started lifting weights the summer between 8th and 9th grade, I believe he was 13 yrs old, to get bigger for football. I do not remember exactly his size at the time, but he was in the neighborhood of 5 ft 6 in tall, and under 200 lbs. By the time he graduated from high school, he was 6ft 4in tall, 280 lbs, approx 16-18% body fat. He was doing 1 arm rows with 120 lb dumbell...the highest they had in the weight room. He had a lot of interest from Div 1 football programs.
I am 5 ft 10 in tall, and his mother is 5 ft 4 in tall. So I certainly cannot see where weight training stunted his growth in any way. He learned self-dicipline, how to work hard, and that results would come with consistency. Important lessons in life. He also got the girls!!!
No reason you cannot start at 13 years old.