What is the advantage of leveling up a particular dish?

For each increase in level of a dish, you earn slightly more Gourmet Points when a customer has that dish. However, it is not one full point extra for each level, instead it is around an 0.2 Gourmet Point increase per level, so once you have a dish at level 2, most of the time you will still see just 1 Gourmet Point increase when serving it, but sometimes you will see a 2 Gourmet Point gain.

Also, the appearance of the dish being served improves as the dish is leveled up.