In Switzerland 82% of PET is recycled. (Note that this number is the percentage that is really reused. Not the percentage that is collected.) The same number for glass is 96%. That means only 44% of glass gets recycled 20 times.
However, this is for reuse, not recycling. Not many glass bottles get reused, most get recycled. Recycling glass is less energy efficient than reusing.
This does not support the OP's case that "Glass is heavier and causes more CO2 emissions because of the increased energy use for transporting them."
There is going to be plenty of transport taking place during those 20 cycles of use and recycle. If the main energy cost of glass is in transport, as he asserted, that's only going to make it less competitive vs. plastic as the number of cycles increases.
As long as transport + washing cost of glass bottles are less than production + transport cost of plastic bottles there will be some number of reuses that make glass the winner.
[1] https://www.palpa.fi/beverage-container-recycling/deposit-re...