He was drunk and wasn't very 'steady' on his feet. [=his balance was not good; he looked like he might fall]
“Everything's going wrong!” “'Steady on', now. It's not as bad as that.”
He held the rail to 'steady himself'. [=to keep himself balanced]
(..) - Dad, I'm here. - Dr. Goldman, I've got you. - Down the stairs. - Easy, you guys. - Everybody just slow down. Keep him steady, Violet. Keep him steady. Dad... it's okay. All right. Careful, careful. (..)1996 Foxfire