Centre of gravity

When two objects are attracted by the force of gravity, they rotate around a fixed point, their barycentre or centre of gravity.

When their masses are equal, the centre of gravity is at the mid-point between the two bodies.

Movement of two bodies with the same mass
(Wikipedia)

When their masses are different, the centre of gravity is closer to the more massive object. If the two objects have masses m1 and m2 and are at respective distances d1 and d2 from their centre of gravity,

$m_1 \times d_1 = m_2 \times d_2 $

Movement of two bodies with very different masses. The red cross is the barycentre of the two bodies.
(Wikipedia)

The volumes of the two bodies play no role in their movements.

A star and a planet rotate around their centre of gravity. As the planet is far less massive than the star, the centre of gravity is close to the centre of the star.

As Jupiter is more massive than all the other planets combined, the Solar System is almost a 2-body system with the barycentre close to the edge of the Sun. Because of the other planets, the barycentre of the Solar System oscillates around the Sun.

This effect can be used when looking for exoplanets: the presence of an (invisible) planet can be revealed by the movement of the star around which it orbits!