That loosing weight can be very important, your body image and how you feel about yourself is also very important.
But I am worried about you!!!

:
You may be trying to be TOO thin. I know that may sound harsh, but for your height and a medium frame you at 135-140 would be ok, if not a little underweight.
I am 5'2, and should be about 120-130 - that's 4 inches different. I always complain about being undertall - not overweight
The reason you may not be able to get the scale to budge is because your body doesn't want to, or CAN'T loose anymore weight because it would be unhealthy.
I am not trying to be mean, I really do want to help, if you need to talk to someone I am here, but at Dr. may be a better choice