The IP of my phone connecting to the IP of Dark Sky is much less precise than the request for GPS coordinates to get block level weather data (the Dark Sky website uses 12.345 digits, so is accurate to block level).

This is where the arguments start to get a bit silly. If the authorities are trying hard enough to find you and your phone is on, the network it is attached to can probably locate you very accurately under most conditions already.

HTTPS is useful, and it should normally be the default for web traffic potentially crossing any untrusted network, but let's keep it in perspective. It's an application layer protocol. It can't protect you against attacks at lower layers.

It's not authorities, anyone setting up a router can peek into this information, and more importantly, tamper with it.

Remember Upside-Down-Ternet? [1]

[1] http://www.ex-parrot.com/pete/upside-down-ternet.html

Right, which is why I said HTTPS should be the default for web traffic potentially crossing any untrusted network.

But who is going to set up a hostile router in an office of five people? Or in someone's home?

Google will put a router in a coffee shop and log everyone who walks by. :-)

Correct. TLS-wrapped protocols don't seek to offer anonymity of the source and destination. They're designed to protect the confidentiality and integrity of data in transit. The best tools we have for anonymity are things like onion routing.