Two dimensional induced quantum gravity with matter central charge $c>1$ is studied taking a careful consideration of both diffeomorphism and Weyl symmetries . It is shown that, for the gauge fixing condition $R(g)$ (scalar curvature)=$const$, one obtains a modification of the David-Distler-Kawai version of KPZ scaling. We obtain a class of models with the real string tension for all values $c>1$. They contain an indeterminate parameter which is, however, strongly constrained by the requirement of non triviality of such a model. The possible physical significance of the new model is discussed. In particular we note that it describes smooth surfaces imbedded in $d$-dimensional flat space time for arbitrary $d$, consistently with recent numerical result for $d=3$.