Starry means full of stars. A starry night, a starry sky, starry darkness.
It describes the sky rather than the stars, and it needs darkness — light pollution has made a genuinely starry sky unfamiliar to most people in Britain, who can see a few dozen stars where their grandparents saw thousands. Starry-eyed means naively idealistic, which is a different and gently mocking use. Note that Van Gogh's Starry Night is what most people picture.
1adjectivestarryFull of stars.
“It was a clear, starry night, and we could see the Milky Way above the hills.”
2adjectivenaivelyNaively idealistic, as starry-eyed.
“The starry-eyed young actor thought he'd be famous within a year.”
starry is a quality of the night sky.
Middle English sterry is star plus -y. Star goes back to a Proto-Indo-European root shared with Latin stella and Greek aster.
Middle English
sterry
English, today
starry
From Middle English sterry, equivalent to star + y.
Etymology from Wiktionary, CC BY-SA