When it comes to optimizing your site there are a few things that should be done, in my book the first is properly optimizing the images that you upload to your site. I always stick with the mentality that I am my site(s), pages, or posts for someone that is on a 3G connection or if you want to go old school for a dial-up modem.
With the speeds of the internet that people are able to get at their home or on their phone, as well as a lot of newer designers out there I think that this has become a forgotten art. There are often times that I have clients reach out to me for site optimization and upon loading their beautiful site it is just dog slow. Digging in deeper 9/10 times their images are not optimized for the web, instead, they are trying to serve 300dpi photos and using HTML/CSS to scale the 20MB 2000 x 2000 images down to a small thumbnail.
By taking some time to properly optimize the images before you upload them to your site using such tools as JPEGmini and/or ImageOptim you can greatly reduce the file size. Before I upload images I personally try to resize them to more of an exact sized image that I am looking for also remember that you can decrease the DPI on an image as this is not magazine quality images that you need to serve as most peoples laptops/displays will render them just fine, even with Retina displays.
Additionally, there are other services that can be used if you do not wish to do the resizing locally, one that I have become quite fond of recently is the ShortPixel plugin. It seems to do a great job of highly optimizing images, rebuilding thumbnails, and also creating WebP images that can be served as well!