Weight Measurement on Mutually Orbiting Planets

[Jonnyb42]

So at the end of the lengthy thread https://www.physicsforums.com/showthread.php?t=404650", a similar but new question of mine arose:

If you consider the Earth rotating, you can measure differences in weight at different points on the Earth (namely, the extremes being the poles and the equator.) I am assuming you know why, etc.
Now if you have two mutually orbiting planets, I wanted to verify that if you measured weight at the point on a planet facing the other planet, and compared it with the weight measured at the opposite side of the planet, they should be approximately the same. (Assuming the diameters of the planets are negligible compared to their separation)
Or also, I am verifying that their revolution does not affect this measurement.

P.S.
I am asking this because when I originally posted the above thread, I had in mind that that measurement was not the same, as if it were similar to a merry-go-round, however I recently realized that this shouldn't be so, and before I went on to think about it more I wanted to verify that I'm right.

 

[D H]

Tidal gravity is measurable. The difference is greatest not between the zenith and nadir points but between the point at which the other planet is at zenith (or nadir) and a point where the other planet is on the horizon. For example, the tidal gravitational effects due to the Sun and Moon on the surface of the Earth vary by up to 0.3 milligal over time (a gal is 1 cm/s²), a quantity that is easily measurable by precision gravimeters.