Hi there- I go through this same thing EVERY time I go to the doctor too! It is such a TERRIBLE head trip! So....I have figured out a safe and simple way to avoid all the pressure and stress. Just refuse to stand on the scale. (I usually say, "No thank you, not today".) I mean they can't MAKE you, right??! The worse thing that happens is the nurse looks like you like you have a "screw loose", but hey, I know I do!

and then it goes documented as "patient refuses weight", in your chart. I find this way easier than putting myself through all the agony....But remember, it might not fly if you are not over 18.
Even at 36, I still HATE the "Dr. weighing me thing". (as silly as that sounds!). I only mean for this to maybe help and put your mind at ease. We all could use a break from beating ourselves up so much!
Hang in there!
Gena