The best way to check if your cat is overweight is to compare to something like this:
and talk to a veterinarian specializing in cats, preferably cats with weight problems. If you are uncertain about the knowledge of your regular veterinarian, seek out a second opinion.
If he does have a weight problem, you will have to put him on a diet. Now, I don't have anything backing this up, but a diet based on activity seems uncertain. How do you know what he is doing all day? Now, it could probably work, but an easier solution is just to reduce the amount of energy he gets.
It is very important that a cat doesn't get starved while dieting. You cannot just calculate the required energy intake for the goal weight and go from there. A cat must lose weigh slowly. A cat that isn't fed properly can develop fatty liver which is very dangerous.
So if you are unsure about the dieting process, contact your veterinarian!