If you read the wealth of comments by people online, you will come to the conclusion that "more healthy" means the same thing as "healthier."
No, sorry, it doesn't. And sadly, there are foreign language teachers being told that it's the same thing. If that were the case, dictionaries would indicate that "healthier" is the same as "more healthy," but they don't.
There is a time, however, to use "more healthy"--but not in the sense of "healthier." Take, for example, a case of you serving your kids healthy food. You want to serve them more of it. So, you say you want to serve them more healthy food. You're not saying you want healthier food that what you have chosen as healthy food for them, you just want to serve more of that type of food. Makes sense?
This kind of thing actually affects comprehension, so I don't think it's one of those things where we should just say, "Oh, the language is evolving and it's okay." It's not like my personal preference of sticking with saying "thee" for "the apple"; comprehension and clarity aren't affected in the slightest by people saying "the" instead of "thee". When you don't use comparatives properly, however, it can defintely affect comprehension.
And whatever you do, don't ever, ever, EVER say, "more healthier"! ;)