Assuming video isn't your main source of content, you probably aren't looking to share a very long video. I just ran a test, encoding the first 30 seconds of a larger video into a 720p MP4 with ffmpeg (with CRF of 28), and the output video is 2.9 MB. That's 1 MB smaller than all the content sent over the wire just by visiting the Medium front page.
But, let's say that you're distributing a 10MB video with your textual content, and your post does get lots of attention and suddenly you need to transmit 30,000 copies of that video. Let's also say that you decided to use a CDN to host your larger static content, such as videos.
In such a situation, you know how much that 30000 visitors cost you? According to CDN Calculator[0], it will cost you, on the low end, $18 that month, and if you where using Amazon Cloudfront as your CDN, it would cost you $30 that month.
If you're more price sensitive though, you could easily use a Digital Ocean[1] droplet as your sole content source, and in that case it would cost you a whopping $5 that month, as each droplet comes with 1TB of network traffic per month. If that's not enough you could switch to a SoYouStart server[2] for $40 a month, each of which has a monthly bandwidth allowance of 250 Mbps, which is 78.3 TB of bandwidth per month.
So no, you probably don't need to resort to 320x260 video in 16 colors : )
[0] - http://www.cdncalc.com/
[1] - https://www.digitalocean.com/products/compute/
[2] - https://www.soyoustart.com/us/essential-servers/