Why do Chinese Takaway shops and restaurants have a fat Buddha?

It is a symbol of prosperity as humans used to only be overweight when they were rich in some fashion. Whether that be in money, food, title, personality, etc... So fatness was looked upon as a sign of prosperity. Same reason that Santa is fat. Fat people where also stereotyped as being happy. And this also applies to this figure which is a Budai which is a particular monk of a particular sect of Buddhism known for being a jolly figure and depicted carrying a cloth sack.
It's not Buddha but one of the Monks of Buddhism who has their own legends. But it is many times called a fat Buddha. lol

Buddha’s statue is something like this

He looks well-fed.

It’s not The Buddha. I forget his name, but it’s someone else. Google it.

that's disrespectful its called Laughing Buddha

Prosperity symbol