It depends. If you have an active breed that you do nothing with, then it may get "bored" and decide just to eat all day long. This happened to a Dalmation we rescued whose previous owners let him get to 40 pounds overweight!
Older dogs are prone to hypothyroidism which makes them prone to obesity. All older dogs should be screened for with with blood tests annually.
Free feeding is just not a very good idea. Not only does it make potty training more difficult, but by allowing them to eat whenever and how much they want, you are giving up of your control over resouces and this plays a role with trying to train.
There have been many studies on obesity and dogs and we see far too many fat dogs for ACL injuries for surgery. The fact that some are so obeses complicates recovery and most end up having bilateral ACL injuries. Along with knees, all joints (especially hips) are adversely affected by obesity. Many small breed dogs that are obese are more prone to disk ruptures in their backs, and is complicated collasping trechea and heart disease.
Studies have found the dog fed 30% less then the "recommend" nutritional amount not only live longer, but have less incidence of arthritis, joint and ligament problems or that these problems occur much later in life compared to those fed the 'recommneded" amount. So less is more.
Also, overweight cats - not good. Many are suseptible to urinary tract disease, diabetes, and liver disease.