Tip: See my list of the Most Common Mistakes in English. It will teach you how to avoid mis­takes with com­mas, pre­pos­i­tions, ir­reg­u­lar verbs, and much more.

When you want to express that the manner in which you eat is healthy, you can do so using the adverb “healthily” (or “healthfully”) or by using “healthy” as an adjective:

You’re fat as a pig. You should eat more healthily.

You’re fat as a pig. You should eat more healthy food.

However, it is becoming extremely widespread to use the adjective “healthy” also as an adverb, so it is not uncommon to hear “eat healthy”, especially in American English:

Didn’t your doctor tell you it is important to eat healthy?

Traditional grammarians say that “eating healthy” is wrong, but considering that there are dozens of books on Amazon that contain “Eat healthy!” even in their titles, I believe you can safely use it without being worried you are saying something unnatural.

Nevertheless, major English dictionaries do not list adverbial “healthy” as an acceptable alternative to “healthily” (or “healthfully”), so it is advisable to avoid it in any kind of formal writing and English tests.