Overtraining is a stress on the body. Enough of any stress is gonna hurt. But...exercise is something you need, most Americans don't get enough, and it shows. You need to get an organised training regimen going. A coach ( a guy you can talk to, outfits like CTS might be ok, but they can't look in your eyes and tell you to take the day off). There are good sources for info, I like the Heart Rate Monitor Book for Indoor and Outdoor Cyclists by Edwards and Reed.
But the bottom line is you want to hammer once a week. All the other rides during the week are either for recovery, or for base building. If you really want to get sophisticated look into periodised training schedules.