I've been thinking about going to metal bottles as well and found the Klean Klanteen 40oz wide mouth on rollback at Walmart for $11, so thought I'd play around with it. What follows is an exercise in gram weenie-ing and OCD.
My plain (not powder coated) bottle, without lid, weighs 6.87oz on my kitchen scale. So you save a little weight going plain steel.
The lid is the biggest issue as it weighs 2.6 oz (my scale agrees with Steve's). A Nalgene lid leaks, but almost any Hydroflask lid fits and weigh less than the stock lid from Klean Kanteen. I purchased a cheap pair of lids from Amazon (
https://www.amazon.com/dp/B078T19RDY), which weighed 1.44oz as stock. I removed the little lanyard, since it doesn't function on the Klean Kanteen, and also removed the grippy rubber ring, since I think that's going to fall off sooner or later anyway. The stripped down lid now weighs 0.95oz. So the bottle+lid weighs 7.86oz.
A 32oz Nalgene on my scale weighs 6.20oz.
A Nalgene holds 5.16 oz of water per oz of bottle weight. The modified 40oz Klean Kanteen holds 5.09 oz of water per oz of bottle weight. When you look at it that way, you can get them pretty close.
Of course, I just put a plastic lid on my metal bottle, so maybe this is all for nothing since I still have plastic elements in the setup. And as far as weight is concerned, we are still nowhere near a Smart Water bottle. But I have always been willing to deal with the weight of a Nalgene for the ability to put hot water in it, so that was the weight standard I was striving for.