While birthweight of offspring is associated with pre-pregnancy body mass index (BMI) and later risk of obesity, its mediating effect between the association of maternal pre-pregnancy BMI and offspring’s childhood anthropometrics has rarely been investigated. This study aimed to examine whether offspring birthweight is a mediator in the association between pre-pregnancy BMI and offspring’s childhood anthropometrics. The study included 1,618 mother–child pairs from the Australian Longitudinal Study on Women’s Health and Mothers and their Children’s Health Study. Children’s anthropometrics [mean age 8.6 (s.d. =3.0) years] were calculated from the mothers’ self-reported child weight and height measures. G-computation was used to estimate the natural direct and indirect (via birthweight) effects of pre-pregnancy BMI. In the fully adjusted model for maternal sociodemographic and lifestyle factors, the natural direct effects of pre-pregnancy obesity on child BMI-for-age, height-for-age, weight-for-age and weight-for-height outcomes were, β (95% confidence interval, CI), 0.75 (0.55, 0.95), 0.13 (−0.07, 0.32), 0.62 (0.44, 0.80) and 0.57 (0.24, 0.90), respectively. The corresponding natural indirect effects were 0.04 (−0.04, 0.12), −0.01 (−0.09, 0.07), −0.01 (−0.08, 0.07) and 0.09 (−0.05, 0.23). Similar results were observed for pre-pregnancy overweight and pre-pregnancy BMI as a continuous scale. Most of the effect of pre-pregnancy obesity on childhood weight-related anthropometric outcomes appears to be via a direct effect, not mediated through offspring’s birthweight.