Abstract Background Use of generalized linear models with continuous, non-linear functions for age, period and cohort makes it possible to estimate these effects so they are interpretable, reliable and easily displayed graphically. To demonstrate the methods we use data on the prevalence of obesity among Australian women from two independent data sources obtained using different study designs. Methods We used data from two long-running nationally representative studies: seven cross-sectional Australian National Health Surveys conducted between 1995 and 2017–18, each involving 6000–8000 women; and the Australian Longitudinal Study on Women’s Health which started in 1996 and involves more than 57,000 women in four age cohorts who are re-surveyed at three-yearly intervals or annually. Age-period-cohort analysis was conducted using generalized linear models with splines to describe non-linear continuous effects. Results When analysed in the same way both data sets showed similar patterns. Prevalence of obesity increased with age until late middle age and then declined; increased only slightly across surveys; but increased steadily with birth year until the 1960s and then accelerated. Conclusions The methods illustrated here make the estimation and visualisation of age, period and cohort effects accessible and interpretable. Regardless of how the data are collected (from repeated cross-sectional surveys or longitudinal cohort studies), it is clear that younger generations of Australian women are becoming heavier at younger ages. Analyses of trends in obesity should include cohort, in addition to age and period, effects in order to focus preventive strategies appropriately.