Answer
If Earth gained mass, it would pull down harder on you, and you "weigh more" as measured by a scale you stand on.
On the other hand, if the sun became more massive, your weight as measured when you stand on Earth would not change. You (and the Earth) are in free fall around the sun. The sun's gravitational pull keeps stuff moving in a circular path around it, but has essentially no effect on the force exerted between the Earth and you.
It is similar to astronauts feeling weightless in free fall (pages 166-167), who are neither pressed against nor pulled away from the walls of their spacecraft by the Earth's gravitational force on them.
