Does obesity affect the performance of policemen?

Answer 1

It probably can - this is the reason that many agencies and departments require their officers to undergo annual physical fitness qualifications to maintain their certification.

There are always exceptions, but as a general rule, an overweight officer is going to have a hard time keeping up with a young fit suspect that is running away through yards and jumping neighborhood fences. After reaching a certain weight, it becomes much more difficult to find correctly fitting vests as well.