Weight? I just took an extra glass screen protector for my 4XL and compared the weight to the new TPU protector for a Pixel 6 Pro and cannot feel a difference. Possibly, I'll take them out to my reloading shed and check on my digital scale but have way too much to do today.
The TPU is .1mm thick, the glass is .3mm thick. Believe me, you will never note the difference in weight.
Not sure about the rest of your post! Are you saying you don't have to use the FPS to open the phone? ("I still can use it without even readding finger prints")
However, it is a non-subject at this time since it appears the only glass protectors I can find all state they will NOT work with the Pixel 6 Pro due to the optical scanner.
I have used TPU protectors years ago, and they do a good job to protect from scratches, cheap and easy to replace. Some of us just like the glass, usually easier to install, last longer and do give some impact protection. But not a choice with this phone.