16 MEGs??? Judging from the way the rest of the computer is stocked, I think you mean 16 Gigs.😉
Does the Facebook shutdown occur with any browser (Firefox, Chrome, Safari, other?) or just one particular browser? Same for weather maps. The only thing that seems to indicate it is not a browser issue is that you also get a shutdown, but only ocassionaly when openig a large Photoshop file.
Also, just curious, with the high level of resources, you have invested in the computer, is there some particular reason you are staying at 10.6.8? I wonder if the problem would happen with 10.8. That is only a thought and not a suggesdtion to go to Mt. Lion. Are the other Apple updates (non OS) all current for your system? I mean things like firmware updates, Java updates, security updates, etc.?
Have you tried eliminating all the plugins and extensions for your browser(s)? Just wondering if there is some conflict taking place. Also, is your browser fully up-to-date?
Does the shutdown happen when you are running a bare bones configuration? I mean with no printers, connected, no scanners, USB flash drives, or anything other than just a wired keyboard and wired mouse connected to your USB, Firewire or video ports. Reason I ask is if there are a things connected is I wonder if they might be putting an additional load on the power supply to where, when it is called to really pump out the power for the more demanding applications the power supply kind of chokes out.