When I walk I feel I put much load on my right leg and I feel its more heavy and weak than my left, I also have lower back pain for 2-3 years!?

Be seen. If you are having back pain and unilateral leg weakness, it would be wise to be seen just to make sure it is not something that could potentially worsen. An mri to evaluate your nerve canal and a detailed exam will likely yield the correct diagnosis. There are many possibilities, but u would certainly get it checked into.