There are in fact physical properties that you can account for to figure out how big of a tower you can create. The bodies of the fish can take this stress for various reasons, so dont worry about that. As far as the water column height goes, prepare yourself for a math lesson
. So, at sea level we are all at 1 atmosphere (atm) of pressure. Thats the equivalent of having a 10.332meter column of water on top of us. There is an absoloute zero pressure you approach as you go higher and higher in that column of water. So, if water stayed the same at all pressures, you could build a 10.332meter tall column of water to have the fish in above an open body of water at sea level. Once you breached 10.332m, the negative pressure would be so great that it would suck air in pas the lip of the tube under the level in your tank and drop the water level back to no greater than 10.322m.
However, there is still another problem. Water at ambient temperature (25C) does not stay liquid at very very low pressures. As the pressure drops, so does the temperature at which water can boil at. Water boils at 25C at 47torr absoloute (sorry, another measure of pressure). So if we convert all that to units we understand, when one gets a column over 9.693m of water at 25C and at sea level above the level of the tank, the water at the top of the column WILL literally boil. Gasses and water vapor are released, and the water column will fall back to 9.693m or less.
Therefore, the theoretical max at sea level is 9.693m but probably a more safe practical max is 8m. Your suggested 1m is perfectly safe and probably wont put too much stress on any properly solvent welded joints.