Well I am just knowledgeable and experienced with computers, you tend to learn how things work. The shared graphics memory thing has been around for a long time for windows. I wouldn't say it's self adjusting, it's a set allocated amount so doesn't adjust (as long as hardware isn't changed). I would say it's dynamic, as it can be used by both the system and gpu. Shared memory questions as well as amount of vram questions pop up a lot, mostly everyone thinks more memory the faster/better it will be. But this is not always the case.
I am not saying the integrated is bad, it will work flawlessly as you have seen for everything except for graphic intensive workloads like games. I would still say it's weak and increasing vram won't help it. The only reason to increase vram is to try to alleviate any lag caused when using large resolutions. But for office stuff or even playing movies, 128mb can handle 1080p (yes 1080p movies too) if the gpu is strong enough.
Just an FYI, here's a hierarchy chart to put its performance in perspective.
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-7.html You'll see the 8200m is near the bottom and again I'm not saying it's bad and will actually handle mostly everything a normal person does. I actually have a laptop similar to yours (slightly weaker actually), 1.8ghz turion x2, ati x1270 128mb, 2gb ram, still on vista although tweaked. And it plays 1080p movies, facebook/flash games and even older games just fine.
But to try to see if you actually can change the amount; is your bios up to date? Otherwise you're stuck with what you have. Some laptops can, some can't; this goes for desktops with integrated as well. It depends if the OEM allows you to change the option as most OEMs will lock just about everything in the bios.