Wine brand owners Constellation Europe and PLB are also among those making positive steps to reduce the amount of glass used to bottle their products, according to the Waste & Resources Action Programme.
Lighter-weight glass is said to be better for the environment because transporting it creates less carbon dioxide than moving standard bottles.
WRAP glass technology manager Andy Dawe said: "It is great to see the wine industry making such progress which will have environmental, consumer and economic benefits."
Tesco's efforts to lightweight its own-label wine bottles will save more than 2,500 tonnes of glass every year and will contribute to the company's target to cut packaging by 25 per cent by 2010.
Morrisons' work with Corby Bottlers to reduce the weight of the bottles used for its Working Dog and William Grove wines will save 200 tonnes of glass per year, while PLB's efforts will save 320 tonnes.
The biggest move has come from Constellation Europe which will save an estimated 2,800 tonnes of glass per year by introducing lighter-glass bottles for its Stowells and Echo Falls wines. PLB's efforts will save 320 tonnes, WRAP said.