I have never seen a table like you are describing. I think there would be a problem in creating something like that. The closest I can think of would be flex at a given length for a given weight. That is not going to be a straightforward answer to your question, though, because all the sides are supported. You probably need a college mechanical engineering text to get the equations to compute the correct answer.
Don't think you are looking to be that precise, so based on your description, I think .090 would be quite strong and not very heavy. You might be able to get by with .062, if the sides are well braced, but I think you might well see some bulging if there is any weight at all. I really don't think the sides would flex at all with .090
You also did not mention what alloy aluminum you were planning to use. If you use one of the high strength alloys, you should be fine (2024, 5052, 7075 -- almost certainly overkill). I'd be a little concerned about 3003, in terms of strength.
For the size box you are making, I don't think the thickness of the aluminum is going to make a significant difference in weight. You could figure it out, but it's probably a couple of ounces at most.
Don't forget, there is a minimum radius for each skin thickness and alloy. Too sharp a bend will break the metal immediately or create a fracture in the longer term.
Also, in addition to, or instead of, making bends, you could use angle aluminum for the edges and rivet the aluminum sheet to the angles. This would be stronger and would never fatigue. However, it would weigh more because of the angles.
Aircraft Spruce has information about aluminum in their online catalog. I have bought far too many things from them over the years.
Hope that helps.