Think about something here folks. All the load from your second floor is transfered thru walls to the same support structure as the first floor (so is the roof for that matter). Now its is possible that your first floor has joists of 10" height and the second my have 8" joist height, so if the wood (pine 2"x8"X8") has the ability to hold the weight (or if spanned across multiple joists) you should not have any problems. Also, I learned a long time ago that the strongest part of a floor is the center, not the edges. You may keep your floor from bending if you keep things close to a wall, but you also introduce shearing between the wall and the joist that only sits about 6" on top of that wall. Now you have traded a possible general bend in your floor(tank in the center of the room), for the possiblity that you could shear a joist and have the entire tank go thru the floor (not likely I think either, but thats the trade).
My fat A$$ is about 300lbs, my oak desk was at least 500lbs (yeah its big) , add my computer, everything in the drawers, my chair, hundred of pounds of books, not to mention the 110 gallon aquarium I have on the same wall in a loft over the living room, and I have zero distortion in my living room ceiling.
Does you floor have a TV, a shelf to put it on, couch, chair, end table ........ piano!!!!, add up the weight with you A$$ on the couch and you my find yourself not worring too much about 1000lbs.
For those of you who have the occassional weekend party, then you know what it is to have maybe 20 people in one or two rooms, I can almost guarantee you have exceeded 2000lbs.
Sry about the rant, but I've seen this question asked soo often that we could use and engineer to give us some explainations that we can make a sticky out of.