I'm not a health expert but I also got the general impression it's really difficult/impossible to lose weight permanently whatever you do, as the body adjusts the metabolic rate and also the hormones that control hunger.
But even without any weight loss, exercise has health benefits. Being overweight doesn't necessarily mean unfit. Sumo wrestlers are an extreme example, but I know some overweight people who can cycle at a fair pace or do other exercise for hours, much longer than some non-overweight people.
Personally I find the "weight loss" argument for activity psychologically not very compelling. It may or may not be correct in an abstract sense, but it's just not what people experience when they start becoming active. If people expect to lose weight or if this is their main aim, there is a danger they get disappointed and give up quickly.
It seems better to me to promote the direct benefits, like generally feeling more energetic and less easily exhausted.
Cycling (especially utility cycling) has the huge advantage that (once you're used to it) it fits into the day and you don't need to plan any extra time, it even saves time. And it's fun and doesn't feel like "exercise", and you can start slowly.