resizing and compressing are two different things.
Resizing is phyically making the image a different size. You can make images smaller no problem, but making them bigger will mean loosing quality. Compressing is the setting used in the jpeg file. When you save a file as a jpeg it will give you a slider for quality. The higher the number the better the quality, but the file size will be bigger and therefore slower to download. A smaller number will give you a smaller file size but at a reduction in quality. About 7 on the scale should give you the best of both worlds,.