The saying, heavy is the head that wears the crown, means, “with authority comes a lot of responsibility and worries.” In other words, kings and presidents cannot be care-free.
This saying is about the burden of power. The crown symbolizes authority. Heaviness is a metaphor for mental burdens, worries, and sadness.
Uneasy is the head that wears the crown is an alternate, though less common, version of this same idiom.