[PlantedRich]

I would not go that far but some of the same. At the second red line, I would go for a 1X2 with the broad side to the front. Fastened with glue to the shelf and screws at each end, this will be plenty to keep the sides from bowing out. Use a good wood glue and be sure to scrape the paint, etc off the bottom of the shelf so the glue can penetrate to real wood not just the finish? Clamping while gluing would be nice.The weight of the tank will be fine since the weight can be supported at the ends only without a problem. That weight can't go down if the corners are supported.
That brings the question of how those corners are built at the bottom. We can't see if the wood at the bottom corners are down to the floor or if they end and are held up by being attached to the trim. If the wood extends to the floor directly, fine, but if not, I recommend adding blocks of wood at the inside bottom of each corner so that the weight is on a stack of solid wood, top to bottom.

 

[PlantedRich]

Sorry, Got a better look now and see that the center upright is a single piece instead of the shelf as a single piece. What I had proposed was a single piece under the shelf left/right but that won't work.
That's a nice old piece that should be saved!! But the warping seems to be not too uniform. At the back of the left there looks to be more movement than at the front. Or is that look from the finish not being applied the same?
From the larger gap at the top of unfinished board and looking at the amount inside at top left, it looks like the whole may be leaning a bit toward the right as we view it? Does it wiggle if pushed left/ right? This might be the major problem and might need the back attached or perhaps a stronger back if it is some of the really thin stuff. Maybe the whole would be fine if pressed back to stand straight up and a good solid back placed to avoid leaning sideways called "racking"? Just some thoughts to check.
The problem with old wood which is bowed is that it resists being pulled back straight without some large clamps like a bar clamp to reach fully across the front left and right.