Before revision:  Le and Solomon (ESA 2020) also constructed Steiner (1+ \epsilon )-spanners of lightness O( \epsilon ^{-1}\log\Delta) in the plane, where \Delta\in \Omega(\log n) is the \emph{spread} of S, defined as the ratio between the maximum and minimum distance between a pair of points.
After revision:  Le and Solomon (ESA 2020) also constructed Steiner (1+ \epsilon )-spanners of lightness O( \varepsilon ^{-1}\log\Delta) in the plane, where \Delta\in \Omega(\log n) is the \emph{spread} of S, defined as the ratio between the maximum and minimum distance between a pair of points.