If you are using weebly you are going to find it tough to take control of site speed.
First of all choose the right image format for the right job. There three commonly used image format for websites:
GIF is the most website friendly, for it generates a much smaller image file than the other two formats. It is best used when the images do not have a lot of colors in it or is black and white.
JPEG is a very commonly used image format. Since it support a color pallet of over 16 million shades, JPEG is often used in photo prints. JPEG files are much larger than GIF.
PNG have excellent color and flexibility. The best part about PNG is that you can create images without a background color, so it can take on any background you have. PNG creates pretty large files, so it is best used for smaller images such as logos and icons.
Choosing the right image format for the right job will greatly increase your website efficiency. In places where you do not need high quality images, you can use formats with small file sizes to achieve the same effect.
Weebly will automatically compress images but there are a number of image compressors available online to help you control the size of your images.
Most importantly, properly sizing images can save many bytes of data. From the Developers at Google:
Sometimes you may want to display the same image in various sizes, so you will serve a single image resource and use HTML or CSS in the containing page to scale it.
For example, you may have a 10 x 10 thumbnail version of a larger 250 x 250 image, and rather than forcing the user to download two separate files, you use markup to resize the thumbnail version.
This makes sense if the actual image size matches at least one - the largest - of the instances in the page, in this case 250 x 250 pixels. However, if you serve an image that is larger than the dimensions used in all of the markup instances, you are sending unnecessary bytes over the wire.
You should use an image editor to scale images to match the largest size needed in your page, and make sure that you specify those dimensions in the page as well.