Why does your weight appear to change, even though you never left earth's gravity?

well, one avenue to take would be...

F = GmM/r2

so... at different altitudes (different distances from the center of the earth, thereby different r values) you would experience different forces... tho' really, if you stay on earth, the difference would be quite small. But technically, weight would be different depending on distance to the center of the earth.

Hello msmiles

Yes, your weight changes with height, as kp2171 already mentioned.
Also your weight changes due to vertical movement (elevator).
Actually : your weight does not appear to change : your weight really changes.
Although your mass remains the same, your weight depends on your mass and local gravity.