As you stand on the equator, with the Sun directly overhead, its gravity is pulling you away from the Earth's center. On the other side of the Earth, the Sun's gravity pulls you in towards its center. Consequently you weigh slightly less at noon than at midnight. However, since the force of the Sun's gravity on a 100-kg mass 1 AU distant is about 0.006 Newton, an average bathroom scale is not going to notice.
And the Earth is slowly curving in its orbit, generating an apparent centrifugal force that decreases your weight at midnight, and increases your weight at noon. Except for a very tiny tidal correction, these two forces exactly cancel which is why the Earth stays in orbit in the first place. This argument would only be valid if the Earth were suspended motionless on two giant poles running through the axis or something.
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.