This is going to sound really stupid. But how do I change my normal force? Suppose I am going to the doctor's and I want to do either of the following


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*Make myself lighter on the scale

*Make myself heavier on the scale


For 2), isn't it just relaxing and let your mass drop?
For 1) how could I do this? Should I maybe exert a force on a table close by? Will that force (from my hand) transfer to the scale?
 A: Lots of ways, none practical (except one).


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*Inhale a lungful of helium prior to stepping on the scale (or conceal helium balloons in pockets or the like). This will have a tiny effect but at least your voice will be squeaky.

*As @FrenchKheldar said, push on a table or pull on a bar. Obviously cheating though.

*Install an absolutely gigantic magnet around the weighing area and use the field to partially levitate your diamagnetic body. This will probably have an undesirable effect on any scales made of metal, though. 

*Weigh yourself on a scales located at the top of Mt Everest, on an airplane, or best of all, on the ISS.

*Similarly, weigh yourself deep in a mineshaft tunnelled into the Earth. 


The practical way would be to increase your metabolic activity and decrease your caloric intake over a sustained period. That and take your keys out of your pocket. 
Seriously - the scales measure the force applied, which under normal controlled conditions  is determined by your mass. So changing your mass, i.e. weight, is the only surefire way to do this.  
A: As you mention for 1), the scale is measuring the force applied on it. When "letting your mass drop" your body experiences a downward acceleration. Consequently, the force applied on the scale will be decreased. This would last only as long as your downward velocity is increasing. 
Eventually you have to stop though, and as you decelerate your downward motion (or, equivalently, accelerate upward), the scales must exert a greater force on you. Consequently, the value on the scales will be higher. 
Try it on a scale, from a standup position, "let your mass drop" and stop when your knees are bent. You will see your weight decreases as you drop, then increases as you slow down to finally reach its normal value.
Similarly, pushing on a table or pulling on a bar above you will lighten the force on the scale, thus decreasing your weight.
