Hill sat out with a lower left leg injury sustained in practice a few days ago but should be ready when Arizona (9-3) plays its Pac-10 Conference opener Jan. 2 at California.
Kellen McCoy had 16 points to lead Weber State (6-7) in the battle of the Wildcats.
Chase Budinger finished with 16 points and 12 rebounds for Arizona, which trailed 36-33 early in the second half.
Budinger had only one field goal before dunking a half-court lob pass from Wise to give Arizona a 58-49 lead with 9:30 remaining.
McCoy's 3-pointer and his short follow-up with 25 seconds brought Weber State within 69-65 before Jamelle Horne hit two free throws to seal Arizona's win.