The two strategies for atrial fibrillation are controlling the heart rate or controlling the heart rhythm. Rate control has been studied and is just as effective as rhythm control. Since your heart rate is below 100, and you are not having any symptoms, there is nothing more that needs to be done in terms of rate control. Some patients are in atrial fibrillation for years. Now, it is possible that the heart can grow weak if it beats rapidly for a long period of time (a condition known as a tachycardia induced cardiomyopathy). I do not believe that is is a concern in your case since your heart rate is well controlled.
With regards to the clotting. There is an increased stroke risk for patients in atrial fibrillation. In A fib, the atria do not contract efficiently and blood can form clots. These clots can leave the heart and cause a stroke when they lodge in the brain. The CHADS2 scoring system is a way to assess the annual stroke risk for a patient in atrial fibrillation, based on other risk factors. CHADS2 is an acronym for Congestive heart failure, Hypertension, Age greater than 75, Diabetes, and history of Stroke. If your meet none of these criteria, your CHADS2 score is 0, and you have about a 1.9% annual risk of stroke with atrial fibrillation. In this situation,aspirin is the prefered method of antithrombotic therapy to reduce your annual risk of stroke.