The phrase "delicately balanced" refers to something that is carefully and finely tuned to create an equilibrium. There are a number of synonyms that can be used to describe this state of balance. "Precariously balanced" is one such option, conveying a sense of fragility and instability. "Subtly balanced" is another, emphasizing the nuanced nature of the balance being described. "Equipoised" is a more formal synonym, meaning that two or more things are in a state of balance or equilibrium. "Evenly matched" is another option, particularly when describing a competition or contest. Other possibilities include "harmoniously balanced," "exquisitely balanced," and "finely calibrated".