More than 2,100 UK households were surveyed on behalf of the Pet Food Manufacturers' Association (PFMA).
Some 62% of dog owners and 72% of cat owners believed they could do little or nothing about their pets' weight, according to the survey.
Only a quarter of respondents said they had ever sought advice on their pets' weight.
"The figures are alarming, and the problem won't go away without a fundamental shift in owners' attitude to feeding their pets," said PFMA chief executive Michael Bellingham.
New shelter data casts doubt on whether the pet population and pet ownership are truly growing.
While the pandemic caused unprecedented suffering worldwide in 2020, the disruptions to dogs, cats and other pets adoption numbers may normalize in 2021.