I battle the same problem, I'll be watching this thread closely. It doesn't really fix anything to know what's going on, but an interesting read on this subject is the
Münchhausen Trilemma. It basically proves that logically we'll never find a satisfying conclusion to whatever is being obsessed about so it isn't worth obsessing over.
Based off the Trilemma, I've noticed that over-analysis comes in two forms: Overthinking (based on condition #2, of the infinite regress), which is the sort of "down the rabbit hole" type of over-analysis, and Circular Worrying (based on condition #1, the circular argument), where you just kind of turn some simple worry over and over in your head all day. Condition #3, the arbitrary axiomatic belief, colors both of those two.
When it comes to recognizing when I've over-analyzing either way, I sort of employ a coping mechanism for the anxiety that the over-analysis causes. It's as simple as it is elegant: if I'm anxious about a situation I'm analyzing, that probably means I'm over-analyzing it.
But what to do?
-For the Overthinking (infinitely regressive) style of over-analysis:
In most situations, the right answer is the simplest and most obvious, it's when the "what ifs" and "but then there's" get introduced to the thought process that things get way more complicated than they need to be. Far-flung contingencies seems so much more likely than they are, the selection bias rears its ugly head as the process of analyzing information turns slave to axiomatic beliefs (hearkening back to #3 of the Trilemma). Pretty soon it's a whole big web of near infinite possibilities.
Here's a tool I use to tear down that web:
1. Write down the problem/worry/thought with a limit of two sentences.
2. Attempt to answer the question using no more than two sentences.
And that can stop the "Rabbit-Hole" type of obsessive thinking.
-For the Circular Worrying type over-analysis:
This is trickier in a way, because the subject of the worry can be summarized as "it is because it is" and that's kind of hard to defeat. I employ distraction to deal with this one. This is why my sig says "Bigger problems: nature's Xanax", because when a distraction (just in my case, a more immediate problem) is introduced, you don't have the luxury of wallowing in this type of overthinking.
It's hard to worry in this way when your mind is thoroughly engaged with something else. Dare I say, even just going and talking to people can be the most effective way to do this since that typically takes a lot of mental resources.
Once broken, this type of overthinking (which, again, is circular in nature) will go away, at least as long as you have something better to think about.
So yeah, I don't know if any of that made any sense or not, I tend to presume too much, but at the very least you might want to read up on the Trilemma and take your own interpretation from it, I found it infinitely helpful.
Or am I over-analyzing this whole thing?
edit: Oh, and I'm Big Pharma's biggest fan, I'm on so many pills AstraZeneca sends me a Christmas card, so that helps too.