Now what happens if you weight yourself in an elevator? Suppose the
elevator is accelerating with an acceleration of 
vertically upward?
This will modify the last example. Now the net force acting on you,
which is the force of gravity 
plus the force of the scale
on you 
should no longer be zero. From the second law
we have
The force of gravity is 
, so solving for ,
we have
And now the rest of the argument is the same as the previous example.
What's the force you exert on the scale, 
? By the third
law, that has the same magnitude as . So the scale registers
a weight of m(g+a).
So if the elevator is accelerating upward, the scale weighs more. If the elevator has a downwards acceleration, then you weigh less.
Your mass doesn't change. Just the force that you exert on the scale.