Thanks @Farcher, this is really clear and useful. Just one final question. Some of the items I want to check are pieces of clothing (undergarment). I wear these underneath my drysuit, so they remain dry while diving. However, if I submerge them in a bucket, they will absorb water, and I think that will change their buoyancy. I considered putting the clothing in a plastic bag, but that would add air). Is there a way I could keep them dry while weighing, or to correct for the water absorbed?

This sounds great. Let me see if I understand. If it sinks: weigh the object in air and weigh the bucket of water with the object submerged. Would I need to take into account the amount of water it has displaced? If it floats: do the same, but add weight until it sinks (and correct for the amount of weight added). Of course, the water in which it is submerged also has a weight. How do I figure that out? Remove the object and weigh the bucket without it? This will be hard with clothing, as that will absorb a lot of the water. The difference between the weights = buoyancy?

This would work for objects that float (or some weight would need to added to make it sink), but not if the object is negatively buoyant and ends up sitting on the bottom of the bucket. The amount of water it has displaced will then only partially capture the buoyancy of the object, right?

Fresh water at room temperature would be fine. I can then always figure out buoyancy in various levels of salinity afterwards.