NLE means non-linear editing. It's what you're doing when you edit video on your computer. As opposed to linear editing, which involves fast forwarding and rewinding tape to find and cut a scene.
Like most 32-bit Windows programs, Premiere Elements will use more memory if you have more memory. To a point anyway.
I have 4 gig of RAM, and I see it using almost 2 gig of that. I don't know if anyone is seeing it use more, no matter how much they have.
Although, when it comes to rendering, that doesn't matter anyway. Rendering is a processor-intensive process. Not a RAM intensive one.
You'll see more RAM used if you've got a longer project and/or many clips on your timeline.
PE0 only takes the memory it needs at any time. You can't force feed it!
The only problem is when editing effects when it wants more than you've got which in your case (with 3gb) would probably be hardly ever.
I originally had 2mb and when I added another 2m it only made a modest difference shuttling up and down a 1 hour long timeline and previewing without stutter.
Windows indicates around 2 mb in use when editing but there may be short spikes of more that don't register on the memory usage display.
I don't think you'll ever see any improvement increasing your memory. The biggest gain I got was splitting it between 3 hard drives.
Watch that your video card is not eating up too much of your available memory in which case you might add another 1gb.