Alot of these responses are half correct. My entire career as an engineer has been working with diffused aeration systems, so hopefully I can shed some light.

Theoretically a bubble's buoyancy is independent of all factors but volume, but that does not by any stretch mean that bubbles rise independently of size. Buoyancy here is the sole upward force that will be equivalent to the volume of water the bubble displaces (which is not constant, as the bubble will compress as it gets deeper with water pressure).

The dragging force that slows the bubbles rise is complicated and is at least partially influenced by the bubbles diameter. At the air/water boundary layer there will exist a surface charge proportionate to the surface area of the bubble and influenced by the salinity of water. That is why the smaller of a bubble you make, the more likely the bubbles will rise slowly giving the same volume of air as the surface area to volume ratio will increase.

For some context, fine bubble air is the most practical for wastewater treatment, using bubbles about 2mm in diameter. This size is ideal as the bubble rises at about 30 cm/s, gives great time in the water for oxygen transfer and still rises fast enough to mix the reactor. In contrast, we intentially use less oxygen efficient coarser air (6mm bubble size) even though the oxygen transfer is half that of finer bubbles and can rise ~10-30% faster, as the added turbulence is particularly good at mixing low solids content liquid reactors.

There are technologies already available that make use of micro and nano bubbles for a variety of applications to hyper-oxygenate the water they are put in. The theory is, the surface area to volume ratio of the air is so high, we find that the bubbles stay in suspension as the buoyant forces don't outweigh the drag forces effectively leaving the bubble in one place in the solution and allowing extremely long residence times for oxygen transfer from the bubble into the water. This technology is primarily used successfully in aquaculture.