the short answer
Cardio vs weights for fat loss is the wrong framing - fat loss is driven by a calorie deficit, not by either type of exercise. Weights preserve muscle, so more of the weight a client loses is fat. Cardio adds to the deficit and improves health. The best program uses both: weights as the anchor, cardio as a tool, and the diet as the engine.
This article is general coaching information, not medical or dietary advice - individual needs vary, and any client with a medical condition, an eating-disorder history, or signs of overtraining should be referred to a doctor or registered dietitian.