I think it's a liability issue.
My mother is a landlord and I can guarantee, if a tank caused structural damage, and she did not give an ok for the tank, she would be suing I would support her doing so.
However, if your landlord says "ok", and puts it in writing, it will be harder for them to sue for damages.
If in doubt, get renters insurance that will cover your fish tanks.
AGAIN, asking MFKers if it will be ok to put your tank on the 2nd floor isn't going to fly in the real world.
BTW, you say everything ok so far. Your floor will not immediately fall through, but it COULD sag overtime.
ALSO: 12 Volt, those Neon Tetras in your avatar got HUGE!!! lol