I found a .pdf listing the specs of your machine... you have 6GB of system ram as it is. Plus 1GB of dedicated ram to the GPU. Honestly that gpu really couldn't make use of more ram very well, however i see no harm in giving it another 1gb of system ram... (if you can control that anyway, check your bios settings, the part where it says "Press 'name of key here' to enter setup") that would be more than enough and you would still have 5GB of system ram left over which would be plenty for games. Even enough for skyrim, system ram wise. dunno how well that gpu would perform in a game like that.
honestly... even if you could upgrade that gpu, it would be costly as other had said, but also your cpu would probably be a bottleneck. of course you could upgrade the cpu but then there's the laptop's cooling limits to consider.
the .pdf i found
http://support.you.gr/catalog/71/71C940D8CBC33147B93B8915C3CE1618.pdf
your current GPU's capabilites
http://www.notebookcheck.net/ATI-Mobility-Radeon-HD-5650.23697.0.html
based on that review above... my best advice i can give you is check to see what clock speed your gpu is running at, and possibly set it to 650mhz if it isn't already. also, if it was set lower, i'd force the fan speed to max since the cooling solution may not be all that good. Also, I'd look into a cpu upgrade. the current one is 35w, so i'd stick to 35w tdp when upgrading the cpu.
Here's a list of CPUs supported by your chipset, though keep it to around 35w TDP. click the "compatible products" link then click "Expand all" link to see the wattage ratings of the cpus.
http://ark.intel.com/products/chipsets/43181
other cpus may work but you'll have to look around acer related forums for that. i'm sure someone on the acer forums has tried upgraded that laptop and could probably give you more info as far as a gpu upgrade goes as well.
