What's the difference between weird content and weirdly content?
In the first case, content is a noun, and so the descriptor is an adjective (weird).
"I'm reading this book about humans who morph into rats; there's some pretty weird content in there."
In your second case, content is an adjective, and so the descriptor must be an adverb (weirdly).
"When Bill's father died, he was weirdly content. It was as if a mass had been lifted off of his shoulders, and he no longer had to constantly prove himself."
For those to make sense, you have to interpret them like so:
Content here is a noun (CON-tent), meaning that which is contained—such as the content (text) of an article, for example. If an article is weird, it will have "weird content".
Content here is an adjective (con-TENT), meaning satisfied or at peace. Someone who is content in a weird way—such as when the circumstances might normally lead to someone not being content—you might be able to describe them as "weirdly content". (I wouldn't encourage you to rush to use this expression, though, as it's a little odd.)