How about sleep medicine? According to this pdf that describes guidelines for fellowship training in sleep medicine, you can combine it with pulmonology or clinical neurophysiology.

On a related note, I think there should be an obesity medicine specialty, if there isn't one already. Like you would probably need some training in endocrinology (diabetes), pulmonology/sleep medicine (sleep apnea€€that Pickwickian body habitus), cardiology (given the risk of coronary artery disease), maybe even PM&R [physical medicine and rehabilitation], and some psychiatry for sure. Then again, given the incidence of obesity in the U.S., what I've basically described is primary care.