Windows automatically sets the size of the swap (or paging file) and it usually sets it equal to the amount of physical memory. So if you increase your physical memory by 4GB, Windows will increase the size of the paging file by at least 4GB -- although in reality you probably need less since you have more physical memory.
I would change the paging file size to a smaller amount: open the system control panel, select "advanced system settings," click the advanced tab, next to performance hit the settings button, choose the advanced tab. Where it says Virtual memory, click the button that says change. Highlight a drive that has a paging file. It will have system managed size chosen and you can see the amount. I would instead use custom and type 2048 in both the initial and maximum boxes, then click set and OK. This will reclaim some HDD space and you won't notice any difference.
edit: also if you do not hibernate your computer you can reclaim a bunch of space.