Hi @George_Papadamou, if you use the Youtube default embeds, they include the play button and the branding, thus it is quite usual for people to NOT use youtube for video backgrounds.
I would recommend the dropbox route or other file storage online, to upload your own videos and load those from that storage.
Check out this article: [Tutorial] How to add a Custom HTML5 Background Video - Webflow Tips - Forum | Webflow
Let me know if you have any questions. It would help for you to start a new post, with the read-only link to your site and the video urls you are trying to use 
cheers, Dave