The Collaborative International Dictionary of English v.0.48:
Stagy \Sta"gy\ (st[=a]"j[y^]), a. [Written also stagey.] Having an air or manner characteristic of the stage; theatrical; artificial; as, a stagy tone or bearing; -- chiefly used depreciatively. [Webster 1913 Suppl.]WordNet (r) 3.0 (2006):
stagey adj 1: having characteristics of the stage especially an artificial and mannered quality; "stagy heroics" [syn: stagy, stagey]