what's the name of the force opposing weight in this scenario?
When the Blue Whale (which was brought into existence when the improbability drive was activated) in "The Hitch Hiker's Guide to the Galaxy" saw the very large blue and white round thing, which was hurtling towards it at an increasingly fast rate, gave it the name "ground" and hoped it was friendly.
The reaction at the surface of the earth is, what we in the trade call, "ground".
imagine "Big imagine" trying to align a GPS at the North/South pole?
I assume you mean IRS or INS?
One reference direction could be towards the "pole star" (vertically up) and the other two at right angles tangentially to the earth's surface. Provided the last two references rotated at the same rate but in the opposite direction to the earth's spin, then you'd be able to calculate any deviation sensed by your reference system with respect to the earth.