How did you come that conclusion. The force on the smaller mass is smaller, and the amount is proportional to the ratio of the two masses. For example, if the mass of one is twice that of the other, the force on it will be twice as great. Newton's second law then shows that the two will have identical accelerations.
I state clearly on the site that I do not do
astronomy/astrophysics/cosmology. However, I have already answered a
question about rotations in the solar system, so you can have a look at
that. For any individual body, the rotation rate is normally determined by
how much smaller or larger it has become over time. For example, some star
may have a certain rotation rate in the "prime of its lifetime", slow down
when it grows to a red giant when dying, and speed up when it collapses into
a very tiny neutron star. Also any interaction with other bodies which
causes a torque can change the rate of rotation, the moon being the best
known. The moon originally had a much larger rotation rate than its current
rate of one rotation every 28 days. The torque exerted on it by the earth
resulted in the change of rotation
Content will be erased after question is completed.