Aquaponics is the phrase given to plants which grown in water not soil. The best thing, in my opinion is NO WEEDS. Sure you get to eat healthy salads and plants from it with very little work and you can eat the fish as well.
This type of combination is nothing new as in the far east they have been doing it for a long time. There they add fish (usually tilapia) into the flooded rice fields. When the rice is ready to pick, the fish are then consumed as well. It has taken the west awhile to catch up but now they have seen the sense in doing so.
Just recently I read about the use of rice fields outside Sacramento in northern California for the rearing of salmon. Yes I said salmon. These weren't allowed to grow to full size but the fry (baby fish) were grown on considerably.
Now you may be thinking, I don't grow rice.
My point is the fish are beneficial to the water with their excrement providing a free fertilizer.
What you can do, similar to our fish farm, is grow the plants on top of the water. The roots will draw up the needed nutrients from the lake, pond, aquarium below.
Obviously these need to be above ground plants, not potatoes, beets or radishes. That isn't to say you can't use this fertile water for those plants you can. Draining some of the water over root crops is a brilliant idea.
Any plants such as lettuces, peppers, tomatoes can be grown in this way. Ground creeping plants such as cucumbers and squash can be grown using this system although they would be best with a frame for support of the veg.
We sell the majority of our plants which we grow through this aquaponics system and they sell easily as they are a deeper green than the ones currently available .
So to recap, no weeds, obviously no watering, and they are constantly being fed with fertilizer from the fish. As you can see, there is no downside.