Edit after comments by OP and clarification of question
A feather and a ball fall at the same rate in vacuum, because there is no air resistance.
As far as we have discovered by observations and the models fitted to observations, there are four forces in nature.
Matter as we have studied it is composed out of atoms and molecules that are held together by electromagnetic interactions. Gravitational forces are very weak at the atomic level and do not contribute to the particular densities of particular masses, after they have formed. The density depends on the organization of the electromagnetic interactions between the atoms. Thus some substances are dense, i.e. more atoms per cubic centimeters, and some lighter.
(this said, gravity collectively organizes matter, as in geological stratifications, and sediments in general, but once formed they are held together by electromagnetic interactions)
Thus, as gravitational forces always act and masses used in gravitation are posited to be the same masses in F=ma of accelerating objects, the combination of the gravitational force and the electromagnetic interactions of all atoms in any form lead to the observed buoyancy:
In physics, buoyancy or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid.
For this reason, an object whose average density is greater than that of the fluid in which it is submerged tends to sink. If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a non-inertial reference frame, which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction.
(Air is considered a fluid in physics .)
In the situation of a ball withing a water container , the center of mass of the system will be falling with the gravitational force, and the system would not change during the fall (although waves might start with the initial acceleration in the water, the buoyancy would be the same)