应该是eat healthily更合适,healthily相当于in a healthy way.
If you don't eat healthily,your body won't work well.
如果你吃得不健康,你的身体机能也会运转得不好.
"Eat healthily," he says,"taking in more fresh vegetables and fruit and less red meat."
“吃得有益健康,”他说,“多吃新鲜蔬菜和水果,少吃红肉.”
We must re-educate people (to eat more healthily).
我们应该对人们进行再教育（使之重视饮食卫生）.那有的人说eat healthy 相当于eat healthy food 能讲得通吗可以这么说。前面问的stay/keep healthy，stay和keep是系动词，所以表语用形容词healthy。live healthy似乎不合适，要么是live healthily，要么是live a healthy life/lifestyle。