@honeysuckle- I can about guarantee that the officers you have seen were slimmer during their physicals. The fitness test is a requirement for becoming a police officer and cannot be passed by someone overweight.
I have an uncle who is a police officer. He said the fitness test is very hard, and you must be prepared for it. It would be extremely hard for an overweight person to prepare for it, let alone pass it. He said everyone knows that the fitness tests are part of police training, and if you are overweight while in training, you have to get the weight off.