What type of file are you editing and what are you saving it as? .pxm, .jpg, .png, .gif, .bmp?
Pixelmator's default file format is .pxm and it is typically larger than most other formats like .jpg because the .pxm file is considered your master file and contains a lot more information about the image, like alpha channels and layers, so it naturally has a large file size. Saving the same image as .jpg loses all this extra information.
If you are saving as a file format like .jpg, file size is affected by compression levels. Higher compression results in smaller file size and lower image quality. If you take an image with a high .jpg compression and save it with default settings (normal .jpg compression), you might end up with a larger file size. Editing and saving .jpgs is tricky business, since the .jpg format is a lossy format, meaning that it loses some picture quality each time you re-edit and re-save.
Otherwise, if you are saving between different file formats, the file size may also change. For example, converting a lossless compressed .png file as a .bmp which has no compression at all. Or saving a 24-bit .png file as a 32-bit .png file, the file size will also increase because you are including an additional alpha channel in addition to the standard RGB.
If you tell us the exact file formats you are using to open and save as, we can give you more details about why your file sizes are increasing.