Being right or left handed doesn't define what is stronger. Consider that is you are doing something detailed with your right the chances are you are holding what you are working on in your left, making your right more accurate and left more used to bearing load and thus stronger.
Over use of one hand means it is more likely to have picked up RSI or other minor injuries affecting strength too.
If the difference is really severe and you can't identify any reason then get it checked out but I know if you were to go to a doctor in the UK with that they would look at you blankly and give you a prescription to pay several £ for a 50p pack of paracetamol or ibuprofen.
