This one came to me on a lark. :-)
Obsessive comes from the Latin "ob" for "over, on, toward or against" and "sid(ere)" for "to sit". The combinative Latin form of "obsidere" then came to mean "to occupy, frequent or besiege". I can see how "to sit on or over" might come to mean "occupy or besiege" c. 1503 as in to take over a place and then set up camp, but how does that come to mean "to frequent", except that it might take a few tries to actually conquer the area. But I'm not really happy with that transition. Apparently, the real transition comes that obsessed in the besieging sense came to be associated with evil spirits, and then c. 1605 that these spirits would possess the individual in a persistent influence or idea. [Ed. note: I'll have so see how this compares to "possessed" later.] Then it's just another little leap from persistent to frequent, possibly as the influence was not as pestering, but still regular, but persistent and frequent is a comparison for another day. From the derivation about the evil spirits, we end up with the current definition of something that occupies ones thoughts, feelings or desires.
Now, in practice, obsessive has some great usages, even beyond the OCD. She was obsessive about completing her wotd assignments. Yes, but unfortunately, I'm not as consistent as I'd like to be, and of my friends with whom I originally engaged in this diversion, they've fallen off a long time ago. His obsessive need for approval actual drove away most of his friends. Obsessive works with people and intangibles such as they derive from the activities or emotions of people, but obsessive requires a degree of sentience. My obsessive computer keeps asking me for my password. No, but cute, as it might raise the level of my computer to AI. My cat is obsessive about licking all the lemon juice out of my pores. Yes. Sentience doesn't require intent; just some degree of cognitive thought. After all, it is the evil spirit compelling the activity. After the attempt on her life, paranoia and depression obsessed her waking thoughts, while memories of the incident obsessed her dreams.
And finally, checking a blog every hour might be considered obsessive. Let me know.