*DISCLAIMER**I AM NOT AN ENGINEER** I am just a dude with a friend who is. So take this with a fist sized grain of salt...
A buddy of mine is a structural engineer and he had a look at my house to tell me what sized tank I could put in the living room. It does matter the way the supports are running, you want to have your tank over as many long floor supports as possible to lessen the weight on each. Ideally you want your tank perpendicular to the supports, as this will spread your tank out on more of them. If you have them parallel, then your tank will be over less supports, say 1 or 2. Whereas if you have it perpendicular, it will be over 3 or 4. It also matters how close it so the load bearing walls in the basement. A tank that's directly over or very close to the load bearing wall in the basement can be bigger than a tank that's dead center in between the 2 basement load bearing walls. It's all common sense stuff that i'm guessing you've at least thought of. You may still be just fine, but a 6' 120 gallon tank running perpendicular to the long beams under your floors will spread the weight out over more beams than your 4' 120 gallon.
So, for my house, which is your typical 1950s home with normal supports, he told me that in the living room (where each side of the room is directly over a load bearing wall, and the room is probably 12 feet wide or so) we could put a 240 gallon tank in the middle of the room and be fine. I'd probably still be nervous doing that without adding supports, but it certainly got rid of any fears I had about putting a 6' 125 gallon tank right near a basement load bearing wall.
Do you have a friend who's a structural engineer? I can tell you that's a weight off my mind (and my soon to be wife's) knowing it's not even an issue.
I don't think your issue is the tank falling through the floor or anything major like that. My understanding is more than it can cause permanent sagging over the long run if it's too heavy.
The sad ending to my story is that my house can support more weight than i can talk my fiancee into allowing in the living room, haha.