Well, I think it's a foregone conclusion that you won't get an actual professional answer that you can take to the bank on an internet forum. But what you will get is some rules of thumb (backed up by any number of tables from lumber manufacturers -- you can find them online) from experienced amateurs. Much of that info was provided above.
Getting the precise load bearing capacity would mean knowing exactly what species of wood you have, the grade, moisture content, any imperfections, etc., plus know precisely how much dead and live weight you might place on it as a worst case. Rules of thumb with margin of safety will surely over-build it for most circumstances.
Having designed and built my own house after having attended an engineering university, though not majoring in structural, and coming from a family of carpenters, I have a pretty good idea of what passes the smell test. And for me, passing the smell test means that it should be built with a big enough margin of safety so as not to even be worried. A structural engineer would tell me that I used way too much wood in my house for that reason. They would have used 2x4s where I used 2x6s, or 2x8s where I used 2x10s, or used 24" spacing instead of 16", or 16" instead of 12". But then, their houses blow over in a 100 year storm, while mine most likely would do fine. For me to feel perfectly comfortable with that fishtank up there, I would put at least 4 2x10s under it fully supported on the walls, and probably if it still felt soft when I hopped up and down on it, I would opt for 6 2x10s not only supported on the walls, but perhaps with an additional 4x4 pillar (or small wall or arch) on each end to reduce the span but still preserve the interior space.
But obviously if you're taking the advice of people on an internet forum, you must assume the risks of any choices you make based on that.