I don’t think you’d actually “notice” the gravity.

Earth would still retain it’s mass, and we’re much closer to it, so it’s lesser mass acts much more on us than the sun’s greater.

Though, the earth would stop orbiting the sun and travel on a mostly tangential path travel nearly radially away from where the sun was, instead of the elliptical path it currently travels.

This is a very interesting physics question that I may look into further. Specifically what would the theoretical acceleration be, due to the lack of the sun? Is it above a humans level of perception?