MOBI files will inevitably be larger than your other book files because of how they work. Each MOBI file actually contains two separate copies of the book in it, one in .mobi format and the other in .azw format. One is for the Kindle, and the other is for the Kindle Fire. Amazon will open the file up and send the correct one to your device, but they require both versions so that they support all of the devices they create.
The only way to significantly reduce a book's file-size that we know of is to reduce the resolution of any images in the book. It's completely up to you to determine what resolutions are acceptable, but we've found that you can safely go down to 150 DPI without any impact on how the image looks, and even lower on most images. 120 DPI is safe for most images except for drawings with fine lines, and 72 DPI is usually fine for pictures.