How heavy are these things?

[Coasting]

Originally Posted by RDNanoGuy

Get a piece of 3/4 ply cut to be a few inches larger than the base of the stand and put it between the stand and the carpet. It will spread the load out over a larger area and prevent the tank from leaning. You can paint it the stands color to make it more attractive.

This.
Don't cut your carpet out
Just ensure the tank is level. I know some people will fill the tank with a few inches of water and then play with it to make sure its level, since waters flat... You can kinda measure the water line from all sides and corners until you're happy with it.
I have a piece of plywood under my stand as well.

Our house is ... 45+ years old, my tanks on the 2nd floor, against a load wall, about 80-90 gallons total system, no issues here.