Will 1x4's and 1x6's be enough for an aquarium stand?
Use 2x material... it's probably cheaper, stronger, and gives you more surface to screw into. (edit: this was based on the original question -- 'use 1x or 2x material?')

1/2" ply would probably be fine, but I'd suggest you upgrade to at least 5/8" ply (or whatever the horrible version of that is in the box stores -- 19/32"?!?) to skin the exterior. Construction adhesive would also be a recommended upgrade. Screws every foot or so.

With a plywood skin on 4 sides and the top, lateral pressure won't be a problem. 

Thicker ply and 2x materials should make this adequate for 1000#, but only you can be the judge. (Maybe we need a bounty to decide what the best testing methodology is... I vote that you take it to a big box store and start loading bags of concrete on it.)

For the top, if you aren't sure that your weight will be bearing on the wood, 5/8" ply wouldn't hurt, either. One cross-brace would probably be all you need to keep the top from sagging and help keep the entire unit from wobbling.

Design-wise, you can make your life somewhat easier by double-thicknessing the legs and lapping them. (Can sketch if needed.) The 2x6 at the bottom could be replaced by a 2x4. (edit: this comment was based on an earlier sketch...)

Edit: let's see if I can add a sketch...


(sigh. after 2 attempts, I can't get it to rotate properly. Sorry.)