The front of the tank stand (where the 2x4 supports are) is way stronger than you need. It'll be fine as is, no worries.
The 2x6 on the open back needs support at both ends and maybe in the middle--so you'll want a base there too. What you have *might* be ok, but when the foundation shifts (and it will if you live in the Dallas area), you might see some separation between the 2x6 and the connected studs. Honestly, I'd be reluctant to build-in a stand for this reason alone. A free-standing design will allow you to shim edges as necessary. But, that's just my opinion. What you have looks ok except for the back which I'm just not real sure about.
Also, I can't see in the pictures how the frame is constructed at either end. Make sure it's setting on supports and not simply nailed to adjacent studs. In general, don't "borrow" support from the frame of the house. The tank stand needs to stand on it's own. (lol).
All that said, I'm not a professional engineer which is really who you need advice from.
Good luck man, looks like fun stuff!