Banned for craving for cookies.
AS for Sins, when it was designed 32-bit applications and OS are standard and 64 bit apps and OS were not. Therefore Sins is a 32-bit .exe. In a Windows 32-bit OS (and yes going Win7 32 bit is stupid but that is another point) with 2 to 4 gigs of RAM there are no issues aside from lag. I never have issues aside from lag. Now a lot of people are going to or at 64-bit OS (I will be upgrading today after I archive important things) and Sins (which is still a 32-bit .exe) runs into a lot of issues as it hits the 2 gig wall. This is a proven issue. Time and time again. You can practically watch it run up to 2 gigs of RAM usage and go boom. Its is an issue with 32-bit programs in a 64-bit environment. Ironically the Original and Entrenchment never hit this wall but Diplomacy did. 32-bit programs can only use 2 gigs of memory. And yes Windows XP can run on less then 1.25 gigs but if it is given that much to play with it will use it. And fast.
Wait WHAT?
SoaSE is a 32-bit app?

Still, I dont think it matters if you're playing it on a 64-bit OS. And thats because I dont think (although not sure) that 32-bit apps are being memory limited when running on a 64-bit environment.
On Win 7 32-bit, windows literally cant see the remaining memory, and will only install and recognize up to 3.25 GB of system RAM. Same goes for all 32-bit Win. But on 64-bit, where there is no limit (I think its up to 32 GB, but it doesnt matter), if you run a 64-bit program, or a 32-bit, its the same thing. Because the installed memory is always the same.
And again, 32-bit Windows can use up to 3.25 GB, not 2 GB. If you want to run other things on the background while playing SoaSE, thats a different story.
About Windows XP, it can run on less than 400 MB, the 1.25 GB you're talking about is crazy, you have to really try to make it to 1.25 gb without playing a game.
Even for Win 7 standards, 1.25 GB is a lot. If want to have your system memory permanently loaded with lots of applications, then stop being cheap and get Win 7 64-bit, and/or install more ram. I guess you're one of those people who dont know what msconfig is, am I right, Ryat? 
Still, even if msconfig is on default, Win 7 will NOT use 1.25 GB of ram, unless you are being stupid and have things running on the background constantly.
And if you can see at task manager your memory loading +2 GB and Sins starting to crawl, then its probably something to do with the game, not your system.
Are you telling me that because Sins is a 32-bit application, and running it on 64-bit makes it unable to use more than 2 GB of ram without using any page file? Thats ridiculous.