If you mean how is a planet's mass (not weight in this instance sorry) calculated than usually scientists use Newton's Law of gravity, such that:
F = GMm/r^2
Then you also know that the centripital force on a given rotating system is approximated to:
F = mv^2/r
then it's just some fancy rearrangements and other data that needs to be collected. In the case of the earth you have:
v^2/r = GM/r^2
r is the distance between the two objects (taken from the center!)
G is the universal gravitational constant = 6.67 x 10^-11 m^3 kg^-1 s-3
M is the mass of the larger body in the system, in this case the earth
v the velocity of a given natural or artificial satellite eg the moons of planets
so we want M, right?
take it such that v = ds/dt, so we know that the distance the moon travels in one day is relatively constant.
there have been laser reflectors planted on the moon so that with laser precision you can now know what the given distance is from the earth's surface, to the moons surface, then take the given respective radii of the two bodies and add that to get r.
G was found by newton and is almost always this value, so no problems there, and now finally you have ...
M = rv^2/G
to know what you weight on another planet, find a satellite (which in the case of venus and Mercury wasn't so easy so they had to send artificial, man-made satellites there), repeat the procedure above and then use Newton's Law once again.
so you know M of that given planet now:
F = weight = mass * gravitational acceleration , where grav. accell = GM/r^2
so finally, G*M(any planet you desire, or even asteroid)*your mass/your distance from the very center of that planet
Sorry for the long winded answer but hope this helps, you now have a relatively long Planetary Weight Calculator, but it does take a little time. Maybe a nice computer program written in MATLAB may help a bit more.
Cheers.
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No. Kepler discovered the laws using Tycho Brahe's data.
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Isaac newton discovered the three principles of planetary motion
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