Getting her on board may require patience measured in years rather than weeks. Considering where she currently stands on health and medical care, there is a decent possibility she is correct that a doctor would turn up something like diabetes or high blood pressure — those are at minimum reasonably probable — yet a huge gap separates her stance on health from the idea of using grey GLP peptides to better both near term and long term health.
Regardless of the GLP drugs, steering her toward a medical checkup stands on its own as a sensible move. At her age and with obesity, her odds of several conditions run above average, and many of those can be treated. On the whole, discovering high blood pressure, cholesterol or diabetes and ending up on a few pills beats waiting until a heart attack or another crisis forces the issue. Even if no weight comes off, simply confirming blood pressure, lipids and blood sugars are fine can head off many of the worse outcomes.
As a rule, people act on what worries them or what is already causing trouble ( rather than on more abstract long term health risk improvements ), so learning what specifically bothers her about her health could be useful, but the clear candidate is arthritis pain, and that is an area where GLP drugs can deliver a great deal of help — partly through metabolic and anti inflammatory effects, but also substantially because less extra weight pressing on the joints means less pain.
If you offer a little encouragement here and there, there is some possibility of bringing her around eventually, though in realistic terms probably not. Should you display clear health gains from GLP's, that could sway her. Ultimately, each person has to make their own health choices, whether or not you approve of them or share them.