An overweight cat might breathe faster because (1) they are overheating which is more likely if they are obese and (2) they have developed type II diabetes which is linked to being overweight.
Other reasons for rapid breathing might include, pain, stress, fever, shock, dehydration, anaemia, lung disease, heart disease and/or a buildup of toxic substances in the blood due to diabetes (mentioned), kidney failure or poisoning. Another reason for rapid breathing with panting is heatstroke.
If your cat is breathing too rapidly at rest you should seek medical attention as soon as possible where x-rays and other tests may be required to identify the exact cause.
Rapid breathing may be another way of describing panting by some cat owners. It is a normal process after exercise and you might also see it when cats are stressed or frightened when, for example, taken to their veterinarian in a car. Panting helps a cat to lower their body temperature because the water on their mouth and tongue evaporates allowing warm air to be exchanged for cool air.
Shallow breathing is associated with rapid breathing. If a cat is breathing shallowly it might be because the motion of the rib cage is restricted. To avoid pain in breathing they breath rapidly and shallowly. The cat may have an injury to the ribs or suffer from the pain of pleurisy. Serum, puss or blood in the chest restricts breathing. This is called pleural effusion and is the most common cause of respiratory distress in cats.
I don’t want to write any more about this because I am not a qualified veterinarian but clearly if your cat is breathing rapidly or faster than usual when they should be at rest in a calm state then something is fundamentally wrong and you should take your cat to their veterinarian. It’s a question of observing and if necessary waiting to see whether the rapid breathing declines. The bottom line is that overweight cats are more susceptible to breathing faster but that does not necessarily mean that they will.
Note: I’m thankful to Cat Owner’s Home Veterinary Handbook, Third Edition pages 297-298 for this information.
SOME MORE ON OBESITY: