The publication The Atlantic also claims that laboratory animals are getting heavier, as well as pets and other animals.
Animals in strictly controlled research laboratories that have enforced the same diet and lifestyle for decades are also ballooning.
and it refers to a research article published in 2010 by The Royal Society:
Canaries in the coal mine: a cross-species analysis of the plurality of obesity epidemics
A dramatic rise in obesity has occurred among humans within the last several decades. Little is known about whether similar increases in obesity have occurred in animals inhabiting human-influenced environments. We examined samples collectively consisting of over 20 000 animals from 24 populations (12 divided separately into males and females) of animals representing eight species living with or around humans in industrialized societies. In all populations, the estimated coefficient for the trend of body weight over time was positive (i.e. increasing).
. . .
Similarly, we examined whether body weight increases were greater for laboratory versus non-laboratory animals. The non-laboratory animals included urban rats, rural rats, and domestic cats and dogs. Again, we compared the meta-analytically derived estimates for each of these groups, and find that the laboratory animals show a greater increase in per cent weight gain and odds of obesity than non-laboratory animals.
. . .
There are multiple conceivable explanations for these observations. Feral rats could be increasing in weight because of selective predation on smaller animals [22,23] or because just as human real wealth and food consumption have increased in the United States, rats which presumably largely feed on our refuse, may also be essentially richer. But these factors cannot account for the findings in the laboratory animals that are on highly controlled diets, which have varied minimally over the last several decades.
. . .
So the study found not only that laboratory animals in a controlled environment are getting obese, but more so than animals in other groups.
The OP also asks
Is the claim ... a consensus view?
The Royal Society states in a page titled Authors
The Royal Society publishes high quality, peer-reviewed journals covering all scientific disciplines. This is part of our mission in relation to the dissemination, discovery and preservation of scientific findings and ideas.