I am the opposite. My left leg is stronger than my right. But I know why: sciatica...
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A year ago I suffered an injury in a Pilates Class that resulted in a piriformis syndrome where the muscles in my right hip were inflamed and squeezing on the sciatic nerve bundle that runs through those muscles. It took 5 months and 4 physicians before it was diagnosed and then it took another 3 months and 3 physical therapists before it was treated effectively. It is now healing and I am working on strengthening that leg to bring it up to the same strength as my left leg. But that will be a long, slow process because some of the major muscles are severely atrophied.

I bring all that up not to whine, but to point out that maybe you should be careful with this: WHY would one leg be weaker than another? They both have experienced the same things: running, walking, climbing, cycling, etc... Since they both experienced the same inputs, they should have the same output. I suspect the most likely cause of a one sided weakness is lack of stimulation from the nerve. Most often that is caused by a stroke -- where the part of the brain that stimulates that area is killed off. But it is also often caused by sciatica where the main nerve that stimulates that leg is pinched. The pinching usually occurs in the back (which is why they had so much trouble diagnosing my injury -- it didn't fit the standard model) but wherever that nerve is pinched, any muscles that it controls will be weaker...

If so, if it is a nerve problem, you don't want to mess with it. As my atrophied muscles will attest, bad things can happen.