with a fixed stare; with set eyes
Describes a person's eyes when they are staring intensely, often with a cold, angry, or determined look. The expression is a fixed phrase; the verb 据わる means 'to be set' or 'to be steady'.
He had a fixed stare and was scary.
Maybe he's angry; his eyes are set.
The expression comes from the verb 据わる (to be set, to be steady) combined with 目 (eye). The exact historical derivation is uncertain, but it is a conventional phrase for a fixed, intense stare.