Yes, the force indeed is proportional to the mass. (Since $F_g=\frac{Gm_1m_2}{r^2}$) ( $m_1, m_2$ are masses of the bodies.)

But this doesn't really matter, because say, for $m_1$, $$m_1\vec a=\frac{Gm_1m_2}{r^2}$$ If you notice, the acceleration of the body is independent of its mass, like you mentioned.

Why do you think this will be any different for a blackhole or a quasar? (Ignoring GR, of course.)

The force you ask for is simply, $$\frac{Gm_{earth}m_{blackhole/quasar}}{r^2}$$ ($r$, being the distance between their center of mass(s).

Yes, the force indeed is proportional to the mass. (Since $F_g=\frac{Gm_1m_2}{r^2}$) ( $m_1, m_2$ are masses of the bodies.)

But this doesn't really matter, because say, for $m_1$, $$m_1\vec a=\frac{Gm_1m_2}{r^2}$$ If you notice, the acceleration of the body is independent of its mass, like you mentioned.

Why do you think this will be any different for a blackhole or a quasar? (Ignoring GR, of course.)

The force you ask for is simply, $$\frac{Gm_\text{earth}m_\text{blackhole/quasar}}{r^2}$$ ($r$, being the distance between their center of mass(s).