@Re-Made Wow. That is a seriously customized, media-rich site. In browsing through the immense library of content, I'd suggest that a video lightbox approach is actually not the way to go (notwithstanding the non-minor issue that imposing no preload on YouTube videos is not a simple task). Even if we could easily make the YouTube videos not preload, given the media library nature of your site, that approach is probably not the best design solution.
In this page on your site: https://www.re-made.life/films-creativity.html, you have Pinterest-style mini content boxes (segregated by alphabetic range) to hold the plethora of videos under the category. A better approach might be more akin to what YouTube themselves does with the "thumbnail preview video" gallery on their main page (https://www.youtube.com/). Notice that they don't use a lightbox approach but rather launch each thumbnail preview video in its dedicated YouTube page. This approach is almost exactly the same as employing a blog to house media content.
The video preview thumbnails on the YouTube main page don't consume much bandwith so you can have quite a lot of them on the page and each one links to its particular full-video "post." Your page appears to employ a categorization tool for the videos which segregates the videos into alphabetic ranges. I'm not quite sure why that was chosen (beyond a way to simply limit the number of videos you see at one time on the page) but effectively, it's a blog type filtering approach with a Pinterest-style masonry grid presentation. If you used an actual blog approach, each video would be its own page entity (rather than being contained within an alphabetic range box entity) and clicking a "read more" type link would take you to the full video post (which could contain the full video embed along with other descriptive data about the video). You could even use the blog commenting feature to elicit visitor feedback about the video right on your site.
Here's a simplified presentation version of this idea with a radio podcasts blog page: https://www.justhereforthebeer.com/podcasts (this doesn't use a Pinterest masonry grid approach but you get the idea - the "Blog" page on that site does use a masonry grid presentation). The podcasts are of several different radio shows and these can be filtered using the blog sidebar radio show categories links. In your case, you are primarily interested in a one-to-one link of the video thumbnail to its full-video post (the category-filtered blog page might be of interest for your various video categories like "Attitude & ID" and "Creativity & Ideas"). There are several blog apps in the Weebly app store that provide ways to present the default Weebly blog page with grid stylization and can echo "above the fold" post content (which, in your case, should not include the video itself) to a main library page).
You might want to consider employing a mega menu or even just using a simple, static page to house some of your menu content (granted, this will require manual updating of page links if you add more static pages to your site). Navigation can be challenging when you go much past the child menu items (the first drop-down items below the parent menu items you see directly in the navigation menu bar). Having lots of grandchild and great grandchild menu items can be a frustrating way for visitors to move around a site. You're better off having a page with a tabular grid of links that, at a glance, will give the visitor a pretty good idea of what's on the site. You can use accordion-style collapsers (like your in-page sidebar sub-navigators) to help keep the menu lists reasonably manageable.
