"overly obsessed" is a correct and usable phrase in written English.
You can use it to describe someone who is overly fixated on a particular thing or idea. For example, "My sister is overly obsessed with her new phone; she won't stop talking about it!".
And that, perhaps, is why I'm not overly obsessed with self-sufficiency.
One woman described sensing last year that her husband, a Manhattan surgeon, was distant and overly obsessed with his BlackBerry.
With Alex Salmond strongly hinting that this will change next May, it would be naive to be overly obsessed with Celtic precedents.
A pigheaded Donald Rumsfeld, overly obsessed with a light footprint, didn't have the forces needed at Tora Bora to capture Osama after the invasion of Afghanistan.
Until then, he had always thought of high-end cooking as overly obsessed with what seemed like meaningless details, but now, from the inside, he saw things differently.
But in translating it to the stage he has become overly obsessed with certain logistics of plot that require lengthy, ultimately tedious explanations by the two leading characters.
While the world overly obsesses about Israel's politics, in Tel Aviv they are way too busy with high tech and nightlife to be concerned with such things.
The reviews criticize the movie as all-over-the-place, trite, too obsessed with Joy's character, overly quirky.
They also present a largely persuasive case that prosecutors and the press (though not the American public) became overly, even weirdly, obsessed with the Whitewater story.
She finds herself free-floating and alone: Donald has developed into an overly practical-minded businessman, obsessed with calling his broker; her closest friend, Zilpha, and her dog, Sammy, have both recently died.
The deontologist now can look overly self-indulgent, so obsessed with the purity of her own soul that she will not sacrifice her integrity for the greater good (see Ridge 2001a).
