George,

The 162 MHz weather channels do not need to be narrow banded. 

NOAA, GMRS, Marine and HAM are exempt from the 12.5 kHz narrowband requirement.  There's a few more services that don't need to but they aren't really relevant for monitoring.

There are some analog ham repeaters that are narrow banded due to congestion and in the eyes of the FCC that was a voluntary thing. With repeaters pairs being gobbled up,  some new repeaters are needing to be narrow banded in order to get a pair coordinated to them.  That's not an FCC requirement but a repeater coordinator requirement.

That's why you may see some 12.5 kHz analog narrow banded ham repeaters listed.

All ham DMR channels are 12.5 khz narrowband by design as well as many other digital voice modes. This is to promote more efficient use of the spectrum.

Hope this helps!

Matt N3IVK