I also have the same three tiered social circle. The first circle I have regular contacts with on the phone, WhatsApp or in person. The second circle tells me when something happens in their life like them getting placed, winning a competition or getting into a relationship.
Facebook helps me immensely with the third group. I can get to know when people are placed in jobs and can then call them up to rekindle the acquaintance (so that I can later get them to introduce me to other people to expand my professional network). If I call regularly (like maybe once each two months) then it quickly turns into silence because we don't know what the other person is doing at the moment, where they are or even what has lately happened in their lives. I can't also talk about common acquaintances due to the same lack of information.
Personally for me Facebook events serve no purpose because if any of us want to plan a meeting we can do so by phone, email or WhatsApp. It does help to plan school reunions though. Facebook's utility to me exists because the people on Facebook keep posting parts of their life on it and I can keep interacting with them without too much effort of having the pain of keeping track of over a 100 acquaintances.
I deal with it slightly by checking the "See updates from these people first" for certain people. It causes them to appear in a cluster at the top of my feed. The best thing is that the cluster is collapsed to show just two stories and I can then expand if there are more.
If anything happens in any of the first two groups, I hear about it because I'm directly invited. There aren't things that I hear about from Facebook, unless it's some club organizing an event or something similar.
How do you* interact with people, generally? Do you talk to them less but see what they post on Facebook?
* By "you" I mostly mean "people who use Facebook for socialization".