I guess GIMP is out of the question, and that leaves two contenders from my point of view:
Paint.NET is free image and photo editing software for PCs that run Windows. It features an intuitive and innovative user interface with support for layers, unlimited undo, special effects, and a wide variety of useful and powerful tools. An active and growing online community provides friendly help, tutorials, and plugins.
It started development as an undergraduate college senior design project mentored by Microsoft, and is currently being maintained by some of the alumni that originally worked on it. Originally intended as a free replacement for the Microsoft Paint software that comes with Windows, it has grown into a powerful yet simple image and photo editor tool.
FastStone Image Viewer is a fast, stable, user-friendly image browser, converter and editor. It has a nice array of features that include image viewing, management, comparison, red-eye removal, emailing, resizing, cropping, retouching and color adjustments. Its innovative but intuitive full-screen mode provides quick access to EXIF information, thumbnail browser and major functionalities via hidden toolbars that pop up when your mouse touches one of the four edges of the screen.
Which one is the easier on system resources is anyones guess. I would try them out both, and see which one fancies you the most.