In 2005, the Scottish Government issued a full environment impact assessment report. The report includes the following finding (at page 31):
Paper bags are anywhere between six to ten times heavier than lightweight plastic carrier bags and, as such, require more transport and its associated costs.
More paper bags = more gas consumption.
We can present this graphically as follows, assuming that paper bags are only six times heavier.
Delivery of PLASTIC bags

Delivery of PAPER bags with same grocery carrying capacity
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