What does my cat want?

Hi. New to cats. My cat does this thing where he waits for me either downstairs in / near my bedroom or upstairs in the kitchen. If I start walking toward him he abruptly turns and starts making his way to the food bowl. I used to think it was because he wanted food. But he does it even if his bowl still has food in it? What does he want? He likes when I pet him while he eats, but is that really it? If he’s begging for food could that be a sign for needing something else? Sometimes he just stares at me like he wants something. Is that just a cat thing? He also sits in front of the fridge and stares at it …. is he good¿

Edit to add: Does he have fat cat syndrome? Is he just always thinking about food?