As someone else said,minecraft is cpu intensive not gpu,also if your minecraft world is not huge (been playing for ages and the world size is too big for the amount of ram you have) then i would look into getting a vanilla minecraft install with optifine as a base line to see what it runs like,if it's still the same in terms of performance then run that new build off of a usb dongle (yes usb dongle) i can run minecraft from a 4gb dongle and the performance is the same,i get about 90fps and a constant 60fps with vsync enabled.
if a new build doesn't run right but runs right off of the dongle your hard drive may need defrag/format and a fresh windows install,if it's all still not running good then still defrag and format and install windows again,you will need to do this to limit the things that could be wrong,usually i have noticed on laptops that begin to overheat,minecraft is one of the first games to get slower and slower and stutter,check your cpu first before anything else i mentioned,check your fan,i would repaste your cpu and give it a clean out while you are at it,you might see a huge improvement right away.