The shape of the weight-for-stature curve versus the BMI-for-age curve

The shapes of the weight-for-stature and the BMI-for-age growth curves differ, as you can see. The weight-for-stature curve shows how weight increases in relation to stature. The 1977 weight-for-stature charts are limited to prepubescent boys under 11.5 years of age and statures of less than 145 cm and to prepubescent girls under 10 years of age and statures less than 137 cm (Hamill et al., 1979). The BMI-for-age chart shows age-related changes in growth and can be used up to age 20. With the BMI-for-age chart weight, stature and age of a child are considered whereas with the weight-for-stature chart, only weight and height are used. 

The shape of the BMI-for-age chart clearly illustrates "adiposity" rebound

BMI changes substantially with age. After about 1 year of age, BMI-for-age begins to decline and it continues falling during the preschool years until it reaches a minimum around 4 to 6 years of age. After 4 to 6 years of age, BMI-for-age begins a gradual increase through adolescence and most of adulthood. The rebound or increase in BMI that occurs after it reaches its lowest point is referred to as "adiposity" rebound (Whitaker et al., 1998; Rolland-Cachera et al., 1991; Rolland-Cachera et al., 1984). This is a normal pattern of growth that occurs in all children.