If the box flexes, that alters internal volume, changes tuning, and generally creates alot of problems. How thick of walls you need is not really dictated by the amount of power to the speaker, or even how hard the speaker is working... its dictated much more by the surface area of each wall. The larger the surface area of the wall, the easier it will flex. A small box, or a box made up of many small sides (like an octagon) is less likely to flex than is a box with much larger walls but with more wall thickness. You could get really technical and do FEA studies, but most people just make sure to over-build the enclosure and know the problem does not exist.
Its a little known fact that speaker enclosures can be designed/built in two different ways. The main criteria for an enclosure is that its resonant frequency (the freq at which it resonates naturally) is outside the frequency range the speaker is intended to perform. In other words, if the enclosure is to house aspeaker that will play 20hz-80hz, you dont want its resonant frequency to be like 60hz. It should be above or below the 20-80hz range. Almost all enclosures are built heavy, with dense materials, in order to lower the res freq to a point that will be inaudible even if/when it resonates. But, you can also build a lightweight but very rigid enclosure that will resonate ABOVE 80hz (to fit my example). Heavy, thick walls tend to indicate an enclosure meant to resonate below the audible freq spectrum. But, in theory you could build an enclosure made of out notebook paper, that with enough internal bracing to avoid flex, would reside ABOVE the useable freq range.
Stick with big and heavy, its alot easier to create. Its not terribly uncommon in home audio applications for the sub enclosure to be made out of, or mass loaded with, concrete.