Answer
If $m_3$ is gradually increased, the center of mass of the system shifts toward that particle.
Work Step by Step
In general, if the mass of a particle increases, then the center of mass of the system shifts toward the particle.
To understand this concept, we can consider the following situations with a system of two bodies of mass $m_1$ and $m_2$:
If $m_1 = m_2$, then the center of mass of the system is exactly in the middle between the two bodies.
If $m_1 \gt m_2$, then the center of mass of the system is closer to the body with mass $m_1$
If $m_1 \gt\gt m_2$, then the center of mass of the system is very close to the body with mass $m_1$
In the Sun-Earth system, the center of mass of the system is much closer to the sun because the mass of the sun is much bigger than the mass of the Earth.
Therefore, if $m_3$ is gradually increased, the center of mass of the system shifts toward that particle.
