First, a review by a vet is important to make a proper diagnosis of any skin (or other) problems.
Beyond that, it is common for overweight cats to have dandruff. There are grooming issues, but also issues with dry skin which is common in overweight cats. The non-technical version as it was explained to me, it appears the body is hording fatty acids to suport all the fat tissue and not directing them to properly produce oils to provide proper skin and fur condition.
(Again, talk to the vet first.) Your cat may need a diet, and foods with more fatty acids. Fishy canned foods are the best, but there are also supplements that can be added. Dry food has less fat and fatty acids since they tend to make the food turn rancid.