Your comment reminded me of a similar experience I had almost eight years ago. I went camping in the desert with a few friends of mine, and in the evening we slept inside these caves that looked out into sky instead of into the horizon--as in the cave entrance was vertical instead of horizontal.
In the evening, from inside the caves, I laid down and looked up and felt a sensation like the one you're describing--"weightless" is definitely the right word. It felt like I was looking into infinity, a literal ocean of stars. The cave was completely pitch black except for the opening that looked out into the sky. I don't have the right words to describe it, but I felt like I was almost pleasantly "falling" into that opening and out onto the star field, despite literally laying in the dirt in the middle of cave in the middle of nowhere.
I quite literally am not smart enough to conjure up the right words for how I felt--and still feel about, all those years later--but I felt this odd comforting sensation that the universe is much larger than me and here I was just sitting in its cradle.