I know that if you are accelerating upward in an elevator, you will have more weight (if you are on a scale) due to normal force of the elevator pressing up into you? Would that happen if you are currently moving downward and (negative velocity) if you accelerate upward? Would that change the effect of acceleration on your weight?
you are moving currently downward,but your speed is decreasing ,that would mean you are accelerating upward. In that case also your apparent weight will be given by,
$n=m(g+a)$ ,where $m$ and $a$ are mass of you and acceleration of the elevator respectively. Only acceleration matters not your current velocity ,this is a consequence of Newton's laws.
You don't increase your weight you increase the gravity on your body while you accelerate away from the Earth and visa versa when you travel towards Earth. Once you stop increasing your speed the increase of gravity will stop. You can stand on a scale and see how much Gs are being applied when you go up.