This is not specific to a single project. When I added a background video (5mb vid) to my Webflow site, I noticed that when I accessed the site on mobile, it would take 5-6sec longer for the page to load. The UI of the site would load perfectly, but the load bar on my device’s browsers would struggle. Using http://www.webpagetest.org (which lets you test your site on a mobile device) I can see that the videos are still consuming data and so even though the video is not being displayed, it appears that the videos are still consuming data. When my sites don’t contain a background video, my pages can load in 1-2sec easily, but with a video (regardless of its size), then my load times jump to 10+ seconds.
I do not claim to be a great debugger, but from what I can gather, something isn’t right. My sites are being exported also, however, I tested with your free hosting and two of the three tests that were done showed that the video was being downloaded so this might not be specific to self hosting.