For Simple or Double (Brown) Exponential Smoothing, a level weight near zero implies that simple differencing of the time series may be appropriate. For Linear (Holt) Exponential Smoothing, a level ...
Crane, D. B., and James R. Crotty. "A Two-Stage Forecasting Model: Exponential Smoothing and Multiple Regression." Management Science 13, no. 8 (April 1966).