Cortisol is the body's main glucocorticoid hormone, made by the adrenal glands. It follows a daily rhythm — highest in the morning, lowest at night — and its job is survival: raising blood sugar for quick energy, sharpening alertness, dampening inflammation, and helping the body respond to threats. A short spike during a hard workout or a stressful meeting is normal physiology.
On a GLP-1, cortisol's most practical relevance is muscle rather than belly fat. Sustained high cortisol is catabolic, breaking muscle protein down when you're already in a deficit. Short sleep is one everyday driver you can do something about: in a lab study, a night of restricted sleep raised cortisol the next evening (Leproult et al., Sleep, 1997 (external link)). Genuinely pathological excess drives central fat, but ordinary stress does far less than "cortisol belly" marketing implies, and "cortisol-blocker" supplements have no credible evidence. See the guide on cortisol, stress, and weight on a GLP-1.