盯住 is a resultative verb compound formed from 盯 (to stare) and 住 (firmly, to a stop). The complement 住 adds the sense of 'fixing one's gaze and not letting go' — you keep watching something intently without shifting your attention. This pattern (V + 住) is common in Chinese for expressing that an action has reached a firm, lasting state (e.g., 记住 'remember firmly', 抓住 'grasp tightly').