Obesity is a rapidly growing public health problem even among the elderly. Understanding the disabling consequences of obesity in the elderly will help us to design better effective intervention management guidelines for the elderly obese. To examine the long-term health consequences of the obese elderly, we present a joint model consisting of two bivariate ordered responses observed at successive time points. The bivariate ordered response model corresponds to the subject's self-reporting health status outcomes including self-rated health and functional status. Although the joint model that we propose is generally suited for use in health and disease research, where the ordered value responses are observed at successive time points, we further extend it by addressing some of the challenges by incorporating the semiparametric features in the ordinal logistic model, by modelling the underlying latent states of health that are associated with self-rated health, by jointly modelling the bivariate ordinal outcomes to mitigate the variability of the single response and by accounting for the non-ignorable missing data due to different reasons through a multinomial logit model. The motivating data were obtained from the Second Longitudinal Study of Aging, which are longitudinal survey data from 1994–2000 providing various useful information on the health status of elderly people. Parameter estimation of our joint model was performed in a Bayesian framework via Markov chain Monte Carlo methods. Analytical results demonstrate the difference in longitudinal patterns of the health outcomes between the two weight groups, validating our hypothesis that different management strategies for the obese elderly should be employed.