Dealing with side loads for heavy-traffic website sometime can be painful. But, of course there are some common practice to deal with this kind of situation. For example, you can take advantage of cache system, offload to other service to reduce server load/bandwidth, or using CDN (Content Delivery Network).
For WordPress-powered sites, you can take advantage from its Jetpack. This free plugin offered lots of handy features to help you work with your WordPress installation. One of them is a featured called Photon.

Give your site a boost by loading images in posts from the WordPress.com content delivery network. We cache your images and serve them from our super-fast network, reducing the burden on your Web host with the click of a button.

That’s right. You should see some big hints there: content delivery network, cache, super-fast network. To activate this feature, just hit the “Activate” button, and you’re set. All your uploaded media files will be served using WordPress.com infrastructure. After having this feature activated, all image URLs in your posts will be modified. For example:

• Original URL: http://domain.com/dotsios300.png
• New URL: http://i2.wp.com/domain.com/dotsios300.png

If you are interested, here is an example of the image header served from WordPress.com network.

HTTP/1.1 200 OK
Accept-Ranges: bytes
Cache-Control: public, max-age=63115200
Content-Type: image/png
Date: Sun, 06 Oct 2013 17:06:28 GMT
Expires: Wed, 07 Oct 2015 05:06:26 GMT
Last-Modified: Sun, 06 Oct 2013 17:05:27 GMT
Server: ECS (sin/47C6)
X-Bytes-Saved: 8597
X-Cache: HIT
X-Content-Type-Options: nosniff
X-nc: HIT iad 90
Content-Length: 46456