I am bulding a 10-15 gal refugium. This will be DIY style due to the location it needs to go in the stand. The 2 sides(left and right sides) will be supported by the stand.
I really wouldn't risk 3/16" acrylic. I used 1/4" just for the dividers on my fuge and they still flex more than I would like. You will never regret erring on the safe side... but if you err on the cheap side you may find yourself VERY unhappy with the results.
I used 1/4 inch for mine , 36x12x12 . With the dividers you will have plenty of stength . I have very little bow in mine . It works out more like 3 12x12x12 that are just sharing the bottom , front , and back panes . If that makes sense .