Tool which can convert web pages from Hanzi to either Pinyin or Zhuyin Fuhao
On Android you could try the "Pinyin Web Browser" app in the Play Store (free and no ads), or "Cantonese Web Browser" for Sidney Lau / Yale.  Both apps print their romanisation with word-groupings, formatted as large as the characters, and cope with on-page changes made by Javascript etc (the two apps also share their bookmarks with each other).  But because every line of text ends up being twice as high as the webmaster intended, sites will break if they use too much "pixel-perfect" vertical positioning (which was not part of Tim Berners-Lee's original plan for the web, but too many webmasters do it anyway).  The app does contain a couple of kludges for the layout code of sites listed on its start page, but one dev can't fix the entire web so YMMV.

The underlying annotators were trained using a variant of the Yarowsky algorithm and therefore take context into account for things like 差 (chāi or chà) and 为 (wèi or wéi) although it still makes some mistakes.  Training data included proprietary documents, so, although the apps are free, the data cannot be fully open-source, and annoyingly CC-CEDICT could not be used because its CC license conflicted with this situation.  But there are some limited English definitions available, or the apps will link to Pleco or Hanping if you have either installed (tap on any word to access the popup definitions and Pleco/Hanping button, unless that word is part of a web link, in which case tapping on it just opens the link as normal).  The code without the data is Apache-licensed if you want to re-train it on another corpus yourself, but the results are not likely to be as good unless you have access to a better corpus than I do.

There exists code for an iOS version, but the Apple developer programme is incredibly unhelpful (1 they only accept apps compiled on a decent Mac with latest OS, not a few-years-old one, 2 they demand 100 pounds a year to subscribe to the programme, universities can be exempt but individual university members cannot, and 3 I have no idea how much extra they invoice for testing new releases).  There are however a couple of established iOS developers who have been given the back-end code, so let's hope they release browsers soon.

As for desktop browsers, I have had some success making "bookmarklets" (like mini browser extensions), but these rely on sending the page to a third-party server to get the pinyin and are therefore not great for privacy unless you can also set up the annotation server on your own machine.  Also an increasing number of sites are blocking the use of bookmarklets altogether in their "Content Security Policy" (CSP), so if you want bookmarklets you now need a browser extension to turn off CSP as well (or a proxy that does the job, but then the proxy has to rewrite secure HTTPS into insecure HTTP; an increasing number of sites have user-side scripts that break when this happens).  There is however a Windows 10 developer who has the back-end code and is making a Win10 "universal app" for both desktops and mobile devices.  In all cases the problem remains of fixing up the sites that are too fussy about layout.  (You could work around this by cramming pinyin into the very small existing space between the lines, but the result would not be half as easy to read.)