I feel like an idiot for not seeing this earlier: you're right; this is the tidal force problem.

More precisely, the lunar tidal acceleration (along the Moon-Earth axis, at the Earth's surface) is about 1.1 × 10−7 g, while the solar tidal acceleration (along the Sun-Earth axis, at the Earth's surface) is about 0.52 × 10−7 g, where g is the gravitational acceleration at the Earth's surface.

In other words, the measured weight of 100-kg human changes from Solar gravity by 5.2 [edit: milli]grams between equitorial solar noon or midnight and equitorial dawn or dusk.