I live in an apartment on the secound floor, I checked with my landlord about having the tank (55gallon) up their and if everything would be ok, they said yes and just to report if any floods happen, right away to them to make sure damage is at minimum... I too was concerced about the weight of my tank... But everything has been fine and nothing bad has happened.
The only bad thing as many people have said above, I can't install a RO/DI unit, as it would be not good for the long run since I'm moving soon to a house, and I have to where to put a rubbermaid trash can except in my dining room when I was going to cure LR, and also use it for water changes, well that was a no go because of the smell and my wife didn't want to put up with with our 3 month old daughter...
Can't wait tell I move into our own house soon sometime this year well be able to upgrade to a larger tank and be able to have RO/DI water for many uses other than tank water...