I have heard this off and on throughout my life as well--most often in a negative context--and I'm still unclear as to exactly what the speaker means by it.
The phrase seems to mean something different to different people, depending on the situation. I think this happens partly because it's one of those phrases that catches on, like, "It is what it is," a catch phrase that's way overused for my taste as it too often gets applied meaninglessly.
To me, the idea that I am thinking too much suggests that I am in danger of the electrical impulses in my brain overheating and causing a combustible relay such as fusion, implosion or explosion. Or maybe this too much thinking is filling my head to the brim with thoughts, causing it to expand. In this case, I might tip over from too many thoughts.
An idea occurs to me, though. If saying I think too much is a way of telling me that I am obsessing or perseverating, then this is helpful news indeed, for once I get going it can be hard to stop. I really think that next time I hear someone say I think too much, I am going to ask what exactly he or she means.