In order to determine whether selection for traits included in the selection index used in a breeding program would increase the mature weight (MW) of females, this study analyzed the association between MW and four traits composing the index: weaning weight (WW), post-weaning weight gain in 345 days (PWG), scrotal circumference (SC), and muscling score (MUSC). Additionally, the genetic relationship of MW with probability of pregnancy at 14 months (PP14) was analyzed to evaluate the association between MW and sexual precocity. The database included 480,000 Nellore animals from Agropecuária CFM born between 1984 to 2012 on farms in the states of São Paulo, Mato Grosso do Sul, and Goiás. The heritability for the six traits and the correlations between them were estimated, with special importance being given to the correlation of MW with the other five traits. The (co)variance components were estimated by the restricted maximum likelihood method. The heritability coefficients were 0.22 ± 0.01, 0.19 ± 0.01, 0.50 ± 0.01, 0.22 ± 0.01 and 0.50 ± 0.01 for WWd, PWG, SC, MUSC and PP14, respectively. The genetic correlations between MW and the growth traits were positive: 0.55 ± 0.04 (WWd), 0.68 ± 0.03 (PWG), 0.07 ± 0.02 (SC), and 0.46 ± 0.01 (MUSC). Selection for WW, PWG and MUSC might be related to an increase in MW of cows. The correlation between MW and PP14 was negative and of low magnitude (−0.03). However, selection for increasing MW in this population of Nellore cattle should not cause genetic change in fertility. The scientific literature on correlation estimates between MW and the PP14 are scarce. Further investigation on the same topic, using different data sets and other approaches are recommended.