When you use a modern browser, your lightweight distro doesn't matter anymore. The web stack is heavy, even if sites are coded with performance in mind.
Very often it is the desktop environment that kills resources on your machine. So if you have a slow computer make sure to pick a desktop environment that is lightweight (Gnome likely won't give you good results). XFCE would be great. I used stock Ubuntu + Xfce for years on an slow chromebook level computer for Youtube videos, social media, Netflix and so on without issues. The machine had 4Gigs of ram and a crappy dual core cpu. Go with Ubuntu + XFCE.
The last time I looked was a few years ago, and slackware (for CLI only) and puppylinux (very, very basic GUI with a browser) were the top contenders. But puppylinux may be too basic for you, it did not support any of the standard browsers by default and likely has some compatibility issues with some sites.
It has a BSD style port system with useflags for optimizations. A very technically precise installation process, and it also boots up faster than anything I’ve seen.
Otherwise, use LFS with either Portage or Pkgsrc.
[+] https://antixlinux.com/download/
I've been too lazy to install/remaster the already downloaded image so far, because mine runs since 76 days 24/7 in RAM :-)
If you're crazy you can even integrate
[x] https://trinitydesktop.org/ and remaster that into your image, but apart from the very customizable look&feel it doesn't make that much sense. OTOH it's not that fat either, very compact, rather.
It also has convenient scripts(via menu) for populating /etc/HOSTS with adblocking lists, similar to pi-hole. That alone makes many sites much less heavy. Otherwise use alternative clients? Like nitter for twitter, and using youtube-dl(g) with mpv for videos like other posters have written? Also installing uBlock-Origin for the parts which aren't covered by hosts-based adblocking. How much RAM do you have?
The latest version of Lubuntu switched to using Qt, which isn't necessarily a bad thing out of context, but it's slower and uses more ram. Lubuntu 18 is probably the latest version without Qt. For more context, Qt is probably something you should use for a general application, not for an OS GUI or default OS apps.
I settled on Ubuntu Mate which is the lightest Ubuntu I am aware of, and I've generally been happy with it for last decade.