So ... I get these results ...
gravitational force of the sun upon the 500 grams at noon is .3021427 grams
gravitational force of the sun upon the 500 grams at midnight is .3020907 grams
The difference is .000052 grams
These numbers are still wrong. Just in case you haven't got them, we should agree (from the website you linked), that force on the 500g object from the Earth is 4.932N, and force on the object from the sun is 0.003N. This means that at mid-day, the object should have an apparent weight of 4.929N, and at mid-night, an apparent weight of 4.935N.
Converting these weights to masses via F = m.a (using a constant scale factor of 9.81ms-2 for the scale), gives mass readings of 502.446g, and 503.058g, between mid-day and mid-night. The difference is approximately 0.6g, but is not observed. If gravity were real, it should be, every 24 hours.
I hold that the apparent mass does not change, because the theory of gravity is wrong. The sun and moon are a lot smaller and closer to Earth than heliocentrism preaches, and it is not gravity that holds them in their courses.
On a second glance, I think that your approach is more correct than mine, as it posits the sun LIGHTENING the weight at noon, while making the weight HEAVIER at mid night.
However ... I finally found a physical discussion of the question which you may be interested in ...
https://physics.stackexchange.com/q...-day-and-slightly-heavier-at-night-owing-to-t
You're welcome, although this is less a physical discussion I'm interested in, and more a disproof of the theory of gravity.
I note in the link that there are lots of suggestions of why the theory may not work, but these seem inconsistent with the other aspects of the theory of gravity (e.g. if Earth is in free-fall so weights remain the same, how can gravity be used to explain the tides?)
There are plenty of holes in the theory of heliocentricity (e.g. all experiments to prove Earth is moving have provided evidence consistent with it being still, the failure of the gravity formula to explain why object weight doesn't change with time of day), just as there are some holes in the theory of Flat Earth. However, the so-called scientists of the day don't want to admit the holes in heliocentric theory, as they don't want people to believe there are reasonable alternatives.