Ah well, I guess my animals must be special!
I haven't had a problem with fat animals, and I feed them as much as they want for the first month or so, and then adjust from there based on their body condition. In fact, I adopted too grossly overweight cats many years ago (19lbs and 16lbs) and brought them back to a healthy active weight (12lbs, 9lbs) despite the fact that they were already 9 years old when I got them and were pretty much couch potatoes.
Currently I have a dog that I can't get to gain weight despite him eating as much as he wants... I was originally feeding him what the package said for his weight and you could SEE (not just feel) all his ribs and vertebrae. The type of food I was feeding him is also known to be very high in protein and fat and cause a lot of dogs to be overweight feeding the package recommendation. I ended up feeding him 2x what they recommended! And no, he doesn't have worms, he just has a super fast metabolism (I actually took him to the vet because he just wouldn't gain any weight no matter how much I fed him). I am hoping that since he has just turned 18 months that he (or at least his metabolism!) will slow down... We clocked him at 55km/h last summer! All he wants to do is run and run and run some more!