I'm going to ignore the issue of weight. Other answers have already covered the reasons why such a city could not exist on Earth, so I am going to assume there is some amount of hand-wavium at work here and simply address the ways that life away from the ground could be made sustainable.
Water collection is the first challenge. A city among the clouds could simply vacuum those clouds up and cool them until they condensed. A single cumulus cloud contains over 1 million pounds of water, or enough to hydrate about 9,000 people for a week. Without knowing the size of the population or what role, if any, weight constraints will play, perhaps collecting a million pounds at once would be a bad idea. Perhaps cloud harvesting is a constant necessity, with the city only taking on enough weight in water to sustain itself for the day.
Hydroponic farming will be your best bet for a food supply. Check out this company, which makes hydroponic farms that fit inside of shipping containers and can provide vegetables for about 100 people each, year round, regardless of outside conditions. Scaling this up would make it even more efficient. A civilization advanced enough to create a floating city could almost certainly improve on this model to grow fruits, grains, and legumes as well. Supplemented by the fishing you mentioned, this would provide a fully nutritious diet for your floating city. Most meals would probably be eaten raw; electric stoves use a lot of power, and open flame would be extremely dangerous and oxygen-expensive. With a diet based on fish and vegetables, this is still viable. Oils and spices could also be produced this way, but they would probably be considered luxury goods.
The hydroponic farms would also provide natural air filtration. Atmosphere is thinner at altitude, so the city would need to be enclosed and to have an ongoing oxygen supply. With proper ventilation, the greenery would constantly convert carbon dioxide into oxygen, keeping the air breathable.
Cotton can also be grown hydroponically, although is it very inefficient compared with other hydroponic crops. A small textile industry could exist in your city. It would probably make sense to use small-scale looming and weaving techniques, since the supply will be low. Clothing would be a sparse commodity, with people having only a few sets of clothes. Cotton can also be used to make paper, if needed. Hemp can also be grown for rougher textiles, like burlap and rope (and recreation ;).
Soap would not be available. Cleanliness would have to be maintained through the use of alcohol-based sanitizing solutions. Again, this can come from plants grown in the hydroponic farms, perhaps the stems and other wasted parts of the plants. There would be an industry to distill this alcohol and turn it into a useful form. There may also be a market, legitimate or not, for alcohol that is suitable for drinking.
I don't see a way to harvest wood, metal, or glass in the air. If these visits to the ocean that you mentioned are close enough to shore, it's possible that sand could be harvested for glass, but that would cut down on the fish yield and probably not be worth it. More likely, hard goods like tools, utensils, and containers would be provided from the ground. Perhaps each family is provided with a set of tools that they are responsible for maintaining. Food and water containers would be re-used for as long as possible
I don't see waste removal as an issue; planes have already solved this problem by simply dumping their waste into the ocean below. I see no reason this solution couldn't be scaled up, particularly since the waste will be almost entirely organic. Since the city still interacts with the larger ecosystem, returning waste water to the ocean will be important for maintaining sustainability.
As with any enclosed civilization, given the limits of supplies and space, population control would be important. Couples would have to be forbidden from producing more than 2 children. If an extraneous child were produced, perhaps there would be a forced adoption to a homosexual or otherwise infertile couple. There could be some drama in this, both for a couple who has accidentally become pregnant with a third child, and for a couple who is hoping for such an accident.
Law enforcement is, again, difficult to theorize on with knowing the constraints of size and population. Is there room for a prison? If not, enforcement would have to be shame- or labor-based . The ultimate punishment, of course, would be expulsion. The altitude of that expulsion, and the state of the prisoner at the time, would indicate the level of cruelty in the society.
I hope this helps!