Golf is more akin to billiards and bowling. It is a skill activity.
To play at the atmospheric level of the pros requires a high level of coordination, nerve and endurance. The game beats you up physically over time.
You can be fat and play at a high level if you are coordinated and highly skilled at the game but don't kid yourself, the pros are quite good athletes, even if they sometimes look out of shape.
You can be fat and play in the NFL and be fat and win the Olympic gold medal in weightlifting.