I still capitalize it. It was a proper noun when it was introduced. I think AP still capitalizes. But it's on its way to lower-case use universally. I capitalize Web too.
They have long since lost their capitalization here (in my field)...I work in the internet domain. Perhaps those who use it the most are first to simplify it?
I can see where at one time it was *more* correct to capitalize. Texting and web use has prompted a shift away from some norms.