Eco-efficiency composite indicators are widely accepted as the ratio of environmental impact to created economic value. These indicators are realistic measures for assessing sustainability performance considering the economy and environment. The weights reflect the importance of indicators to the aggregated environmental impacts. Estimating the relative weight of indicators is highly subjective, and therefore the search for a single unique weighting method has been going on for years. The regression-based weights are one of the most recent trends in sustainability modeling. Since these methods are designed initially to investigate the impact of multiple variables on a response variable rather than to estimate weights, some drawbacks are associated with their potential to provide proper weights. This paper presents a novel weighting approach integrating linear mixed-effect models with Johnson's relative weights to address these drawbacks and provide meaningful relative weights for eco-efficiency composite indicators. The proposed approach's operational and computational procedures are illustrated using a real example, and the eco-efficiency of food consumption of 38 countries is estimated for the period between 1990 and 2012 using a consumption-based sustainability accounting method. The findings have shown that energy use and GHG indicators are the most critical contributor to global food consumption's environmental impacts. The country-based eco-efficiency performance in this work has shown that China, India, and Russia are located in the low eco-efficiency score class. The Spatio-temporal analysis downgraded the geographical location's significance on the trends of eco-efficiency behavior in time and space. On the other hand, it revealed the different types of emerging hot spots over the world.