There is growing literature on applications of biodemographic models, including stochastic process models (SPM), to studying regularities of age dynamics of biological variables in relation to aging and disease development. Alzheimer's disease (AD) is especially good candidate for SPM applications because age is a major risk factor for this heterogeneous complex trait. However, such applications are largely lacking. This paper starts filling this gap and applies SPM to data on onset of AD and longitudinal trajectories of body mass index (BMI) constructed from the Health and Retirement Study surveys and Medicare-linked data. We found that APOE e4 carriers are less robust to deviations of trajectories of BMI from the optimal levels compared to non-carriers. We also observed age-related decline in adaptive response (resilience) related to deviations of BMI from optimal levels as well as APOE- and age-dependence in other components related to variability of BMI around the mean allostatic values and accumulation of allostatic load. SPM applications thus allow revealing novel connections between age, genetic factors and longitudinal trajectories of risk factors in the context of AD and aging creating new opportunities for understanding AD development, forecasting trends in AD incidence and prevalence in populations, and studying disparities in those.