permitt a small quote:
"But Einstein pointed out that a free-falling object has no weight, even if it is in the presence of a gravitational field. I'm not sure what different people make of it, I could never find a clear explanation for the fact, but to me it seems to suggest that, contrary to appearances, a free-falling object is not accelerating at all."
i'm sure you know this, it is an easily over looked fact. weight is not an intrinsic property of matter while mass is. a given mass will have a different value of weight measured depending upon the envirenment in which it is weighed. example my weight on earth will have a greater value than my weight on the moon but my mass will remain the same.
there would be no way to measure the weight of a free falling object since the device you would be using to measure that mass would also be falling free along with it. objects fall at the same rate regardless of the value of thier mass. example bowling ball and marble dropped off leaning tower.
acceleration is just the rate of change of velocity with respect to time, in short it is only motion changing with respect to time. motion is relative hence acceleration is relative so any free falling object can in fact be considered as not accelerating at all, that is if you want to and you balance the rest of the accounting sheets involved.