Midnight Special is a good example of something with a fairly high Weird Level keeping grounded by restricting it to fairly minor outbreaks and keeping reactions to it very human. (Until the end, anyway.) Before that, the biggest Weird flag is really the way the sect women dress being lifted from a the FLDS while the men are pretty plain - a bit of real-world Weird that doesn’t quite fit this particular group.
Michael Shannon is pretty reserved as the kid’s father, Adam Driver as the government theorist is gawky but not super-weird. People have been comparing it to Spielberg, and the best comparison point there is probably Close Encounters Of The Third Kind. (Including the until the end caveat.)