If the entire concern is over leeching from the container into the water, then what you need is an inert surface that won't leech. Stainless steel is just as inert as glass for all practical purposes and it can be made lighter than glass because it is so much stronger that it can have much thinner walls, with the added benefit of not shattering if there is an impact.

If you are very sensitive to changes in how water tastes, stainless steel still ought to pass muster, but my taste buds are not yours, so you might be able to detect some metallic taste that I cannot.

My own thought on the subject is that avoiding ingesting or inhaling all petrochemicals is utterly impossible in the world we live in. If you live in a city, you are exposed all day long, every moment. The added risk from a plastic water bottle on a backpack is not going to change the odds of unwanted health effects enough to matter. There are much broader and more meaningful changes you can adopt instead.