I think you're both right, just talking about 2 different things. The order of the weight doesn't make any difference when it comes to the vertical load supports. The 4 soup cans all weigh the same to the table they're sitting on, no matter which one is on top.
Having said that, the stability of the stand very much does depend on where the weight goes, since mass with a higher center of gravity is more likely to keep moving if/when a horizontal displacement is imposed on it.
Wood is crazy strong in compression, so if the weight of your tanks is resting on the wood supports, things are pretty solid. I found that a bit hard to do for the lower/middle levels, so ended up using lap joints for the front and back cross supports, then some lag bolts for the two shorter end supports on a 60" by 22" 2 level stand made from 2x4's with 1/2" plywood cut to fit for both shelf levels.
FWIW, I messed with making a three level stand from wood, and couldn't find a happy medium on the vertical spaces. The lower shelf was too low if I wanted to see the upper tank very well, and if I moved the lower shelf up, the upper tank was at or above my eye level, and it was even harder to imagine working in a tank that high up. My first shelf now is about 22 inches off the ground, and the top shelf is about 48 inches high.
This changes some if you get a metal stand fabricated, because the cross members can be MUCH thinner, so you don't lose a bunch of vertical space to multiple 2x4's. Good luck and keep posting. Love to see what you end up with.