How are buoyancy and gravity related

Gravity exerts a downwards force on all fluids.
The reason that any given part of the fluid stays still is that the upthrust around it is exactly equal to its weight at all times.

When an object DISPLACES this piece of the fluid then the upthrust still exists but the mass of the fluid does not.
This force is the buoyancy of the object. So it is caused by gravity acting on the fluid around the object.

With out gravity there would be no buoyancy. In order to be buoyant you must float upon the water. If gravity did not force you down on to the water you could not float on it. You would just float away like a balloon filled with helium. In fact the water would be just floating around also with out gravity you could not even have a pool of water never mind float any thing on it. So the relation ship is a strong one and necessary to both party's involved.

They are both forces.