Lighter in day, heavier in night?

Refer the diagram.

Weight is due to gravity and you have weight due to any celestial object in your vicinity and is proportional to the mass and distance between the objects.

Your weight is predominantly due to Earth, however you have weight due to Sun as well (though small due to the large distance)

At 12 noon, weight of a person = weight due to Earth - weight due to SunAt 12 midnight weight = weight due to Earth + weight due ot SunHence you should weigh slightly heavier in night????

However it is not so! Why???