Good question... not sure. The problem is that the weight is what is distorting the base on the uneven surface. Unless the weight is on it, you are not going to get the distortion.
My gut is telling me that if you shim the stand between the stand and the floor with the tank empty, you should be able to fill it and have the tank stand maintain its' integrity unless the floor moves. However, check the stand all around because tiles are uneven and the bed they sit in is rarely flat (one tile slightly higher than the next).
You need to be a little careful that you don't lift the stand though. The shims are generally wedge shaped and if you excerpt pressure as you shim you can lift the stand and then the previous shims will be loose.
But, we are also assuming the stand is square, which isn't a good bet. You might try to identify the vertical supports and, while the tank is full, take the support in the area where there is a gap and drive a shim between the floor and the bottom of the stand. Allow the wedge to move the support up until you can't get a card in any more. Then you can check the rest of the run and hopefully the new wedge won't have increased in height too much to allow a gap in a different area to form. That might be the easiest way.
