Why do i feel weakness on my right thigh when running?

Some thots: Perhaps you have a mild femoral neuropathy, and could be case if you have diabetes. Maybe you have lumbar stenosis which is afflicting the l-3, 4 level on right. Perhaps, your problem is not motor, but sensory such as compression of lateral femoral nerve at hip. If any of the above are mild and early, the exercise exertion may exacerbate the underlying problem. Maybe notify your doc for advice.

Thigh Weakness: Interesting problem. This can be related to the joint and give way due to low back, hip, or knee issues. Also neurologic problems can present like this as well. Occasionally a stress fracture can also cause "weakness" due to pain. Runners are often uncomfortable and a use to "tuning out" pain. I would have it evaluated. Make sure you go to your doctor in running clothes with your running shoe.