It's kind of funny as a web developer because for the longest time Apple seemed to be the one pushing the mobile web forward but now that web apps are reaching for feature parity with native, Apple's initial momentum seems to be ancient history.
It seems Apple still thinks of the mobile web as a content delivery platform rather than an application platform. Their proprietary additions (mostly CSS) largely focused on making things prettier, their rationale for opting out of standard features (e.g. autoplay) often only work under the assumption that the only use for those features would be in the context of traditional content pages.
You want an app? Develop for our walled garden we tightly control to offer our users the best possible experience. If you want it on the web, stick to creating content our users can consume in Mobile Safari, our app for reading websites.
Twitter's native app is heavier than their web app because Twitter has historically filled the native app with junk (like a fullscreen video just for the login screen, "moments", "highlights", hijacking browser URLs, a bunch of ads and ad tracking, etc). Facebook does the same, to an almost silly degree - https://news.ycombinator.com/item?id=8162342
The Twitter client could easily be ~3MB on Android, for instance, if they just stripped the garbage out. And similarly, if you take a web app, and embed all that same junk into it, it will suddenly be a heavy download too.