I dont want to seem overly optimistic here, but look at it this way. A 1400 lb load spread evenly over 4 feet will rest on 4 floor joists (assuming 16" centers). That spreads the weight over those joists to roughly 350 lb per joist, based on the reasoning that youre stand has a flat bottom roughly the same size os the tank, and not 4 legs. Would you worry about a 300 lb person walking into youre house? To get more dramatic, how about that person bouncing up and down on one foot? That would certainly be more damaging. What you CANNOT do is put the tank lengthwise over one floor joist. this would certainly create a sag in the floor at best.
That being said, I would still recommend building a load bearing wall (better yet a room, Hint) under the floor joists that will be bearing the weights, but its not a high tech structure. Nail a pressure treated 2x4 to the floor nail a header up and toe nail your 2x4's in tight. Nail a firestop in between each vertical 2x4 to prevent them from bowing and you are done.
Personally, this seems like the best reason Ive ever heard for having a room in the basement for your filtration and a sump.
I'd be glad to get more detailed if you think it would help.