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From my layman perspective, yes the measured gravity would be double it's original value if measured from the same place.
Gravity is an [edit: inverse squared] function, so it gets weaker at an exponential rate as you move away from the source. But even if it's a value of 1.0 at Earth's surface and .02 at some distant point from Earth, doubling Earth's gravity would double both values to 2.0 and .04, respectively.
Gravity is not exponential. It is linear with mass and inverse square with distance.
Thank you for the clarification. Best way to get the right answer is to post the wrong one.