Nineteen per cent of cats were classed as obese with 20 per cent being considered slightly overweight.
Sainsbury's is warning owners that their pet insurance could be invalidated if they do not take proper care of their pets, which includes making sure they do not become overweight.
Sainsbury's pet insurance manager, Neal Devine, said: "We are seeing a worrying percentage of cats and dogs being taken to the vet who are overweight.
"People often think they are being kind to their pet by giving it treats, but being overweight can influence and worsen many medical conditions."
Osteoarthritis is the most common medical condition among cats and dogs that can be linked to obesity.
This is followed by heart disease/failure, kidney problems, type 2 diabetes and respiratory disorders.
Meanwhile, the Norwich Evening News reports that the Catton Veterinary Surgery is offering £15 health consultations for dogs after staff noticed an increase in the number of obese pets.
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