@criver Well, you're not exactly using much fuel in your sleep/energy saving mode. It's gotta go somewhere, and fat is just the place it wants to be if you don't use it. That and this is just an extremely common mom thing to say in manga. If I had a nickel for every instance I've seen, I'd just be buying my manga instead of slumming it on places like this.
@Glomoro Sure, you are using less energy during your sleep. Your total daily energy expenditure doesn't change based on whether you eat 0 hours before sleep or 5 hours before sleep however. So you will store fat anyways provided you are in a caloric surplus, or vice versa, you will lose fat if you are in a caloric deficit. Feeding time should be a non factor, or a very minor one.
This manga specifically appears to not have an official translation. So you'd likely still be reading it here, unless you read Japanese.
@criver The point is mostly the second thing. I was just prefacing with the logic I expect is behind this common occurrence. The phrasing is quite often something like "If you go to sleep like that you'll turn into a cow," so it's probably got some roots in an idiom from Japan. Idioms and old wives tales, not exactly bastions of scientific reasoning. But boy, do they get around.