While doing squats standing on a weight machine, I initially thought that while I go down, my mg force will be greater than the normal reaction the ground will provide, hence my center of mass is going down. Now the weight machine can only measure the Normal force on it, which should be lesser than my real weight, but when i actually tried it out, i found out it shows I weigh more while going down and less while going up. What's going on?
On the downward part of the squat, your legs are, in essence, letting your upper body fall toward the ground in a controlled manner. Your legs must then stop that controlled fall before it hits the ground.
On the upward part of the squat, your legs propel your upper body upwards, and gravity then slows its ascent.
A good comparison would be an elevator ride. Imagine that you enter an elevator at the top floor of a building and ride it down to the ground floor while standing on a scale. Once the doors close, the elevator cable lets the car fall a bit before bringing it to its usual downward speed. There is a short-duration acceleration (downward) that makes you feel a bit light. If you watch the scale as the car starts moving, you will actually see your "weight" decrease.
As the car approaches the ground floor, the cable must slow the car's descent. There is a short-duration acceleration (upward) that makes you feel a bit heavy. If you watch the scale as the car starts comes to a stop, you will actually see your "weight" increase.
While doing squats, you are most likely seeing the scale's reading at the end of your body's journey upward or downward, giving you the counter-intuitive measurements you have observed.
Try doing your squats very slowly to see if you get the same result.
I suspect you might be observing the effects of phase lag due to the frequency response of your weight scale. Phase shift, ideally defined for linear systems is a behavior of the system that causes the system output to respond with a delay that depends on frequency. The scale has a specific frequency response and you may just be driving it faster than it can respond.