Yes, it's hard. But not impossible.
the problem is how do you quantify a post as "meaniful", you can't give the tools to users, because they well probably abuse it, so you'd need an advance algorithm that can both understand your interests, as well as the context of posts, and from that, deliever to you what you find most important.
this is no easy feat by any means.
Similarly, things like Google Search and Siri might have seemed impossibly hard some years ago.
All you have to really do is simulate the human brain that will be potentially reading a tweet, and see how he/she feels after virtually "having have read" the tweet and see if he/she feels regret for spending the amount of time on it, or joy that he/she hadn't accidentally missed it. Or better yet, simulate the expected life outcome based on having read/not read the tweet and see which potential outcome is better.
Since the above accurate solution is hard, you can use estimation and various heuristics...
Perhaps see how many seconds people on average spend looking at said tweet (vs. others), how often the author tweets (i.e. rare tweets should probably be valued more than very common ones), whether it's a reply to someone, a very highly retweeted tweet... and I'm sure there are more indicators that differentiate high quality, valuable tweets vs. the mundane ones. Just off the top of my head...