If you have many images used as texture files, check to see if the images need to be as large, in the max scene, as they are in their original version.
For example, maybe you have an image whose original size is 1024 x 1024, but, you are using it to texture something very small, such as a door knob. If this is the case, then reduce the original image to 256 x 256, and re-apply it in your scene. It won't make a difference to your scene, but it will make a big difference to the texture space size in rendering the image, and it will make a big difference to the *.fbx file. If your scene is calling many big images, that do not need to be this big, it will make a great difference in your exported *.fbx file size.