I don't wanna derail here, by my inner dork is winning the fight.
"is 1/4" acrylic half the strength of 1/2??" Well, close enough to it not to bother arguing much.
"Are 2 sheets of 1/4" the same as 1 sheet of 1/2"??" NO. There are several reasons why. In an ideal world with simple rules and a lot of assumptions about things being exactly flawless and perfect, yeah, they'd be the same, but there are a few things that prevent that.
1) Your sheets will not be dimensionally perfect. When you weld them together at the edges, one will be warmer than the other, or crooked, or there will be a tiny hair between them, meaning that you now have two members beside each other bearing the load, but only one of the sheets will take that load until it deforms enough that the other sheet is also loaded. Acrylic stretches a bit, but it will still mean that there is more stress in one of the sheets than the other, and thus that sheet will fail before the other one.
2) Acrylic is a brittle material, so surface defects weaken it. The deeper the defect in relation to the thickness, and the sharper the tip of the defect, the more it weakens the sheet. Two 1/4" sheets have 4 surfaces instead of the 2 surfaces of the 1/2", AND the sheets are thinner in relation to the same sized defect, so you are twice as likely to have defects, and they will have a larger effect each on the overall strength of the sheet. You are also likely to trap crap of some description when you laminate the two sheets, which will generate point loads and create more defects.
3) I believe chompers already pointed out that in bending, the fact that the two sheets are loaded in opposite directions will cause them to buckle or stretch and slide past one another. Imagine picking up a stack of paper and you get the idea.
These effects are small, especially since you will not be getting anywhere near the yield strength of the material on the top of the tank, but if we're going to make the comparison, we might as well be anal about it, right?
"is the joint stronger than the acrylic?" NO! Even if you use a glue that hardens to a stronger substance than the substrate, it's the bond of the glue TO the substrate that is difficult to achieve. If you use a glue that soaks into the substrate and hardens to stronger than the substrate, like some wicking wood glues, then yes, your joint, and the substrate in the immediate vicinity of the joint will be stronger. (some kids in my physics 11 class used this principle when we had to build balsa wood bridges and soaked their bridge in cyanoacrylate glue.) However, bonding acrylic is generally done with a solvent. So you take your nicely arranged cast molecules, stir them up with a chemical, mash them together, and then let the chemical evaporate. No matter how well you do this, there will be some chemical left, some tiny air bubble, some flaw, some incompletely blended molecules somewhere. Sometimes seperating acrylic joints forcibly causes the substrate to break before the bond does, but this is most often caused by the way the force was applied, or some other existing flaw in the material. Maybe the 2-part structural plastic adhesives like weld-on 42 will bond and harden to a stronger joint than the surrounding material, but you can hardly count on this to add any strength to the panel.
OK. It's all out now. /derail
