I'm facing a similar situation. Conveniently, I'm a construction inspector and have worked for an engineering firm for half my adult life. Here are a few things I've come up with.
My situation: I have a pair of 234 gallon aquariums I'm building a rack for that allows them to stack. Lets call it 6,000lbs. for water, aquariums, stand, sand, decor, etc... The tanks are 6' x 2.5'. The stands spread that out to 7' x 3'. So that's between 285-400 psf (pounds per square foot). We test soil bearing for homes all the time. Foundations typically require 2,500 psf with slab area being 1,500 psf if they did a sloppy job. So they slab floor is plenty strong to hold my tanks.
I suggest running the numbers for yours, but I'd be shocked if you exceeded a safe threshold.
As for the carpet...
Check for the tack strip. Not only will it throw you out of level, more importantly it'll throw off your weight distribution and cause a concentration point.
The carpet will compress, and will do so rather evenly. I don't see it being a problem at all structurally.
That said... skjl brought up a great point about mold. I'm struggling with that same decision myself. I don't think there is a "right answer" but... after himming and hawwing... I'm keeping the carpet. While putting a couple of other moisture controls in plan in place (tanks sitting on 3/4 ply, ply oversized to catch spills, dehumidifier hard plumbed for constant use).
Good luck and keep us posted!