Upgrade Wheezy to Jessie - how?

I have a BBB running simple (mostly python) monitoring applications.
It's currently running Debian Wheezy and I guess I should at some time
in the next few n=months (years) upgrade to Jessie.

What's the most straightforward way of doing this? It's a headless
system but (when I'm at the place where it's running) I have
reasonably good/fast access to the internet from the LAN where it is
running.

On Fri, 24 Mar 2017 20:56:27 +0000, Chris Green
<cl@isbd.net> declaimed the following:

What's the most straightforward way of doing this? It's a headless
system but (when I'm at the place where it's running) I have
reasonably good/fast access to the internet from the LAN where it is
running.

  Is it running off the eMMC, or off an SD card?

  In either case, I'd probably recommend creating a bootable Jessie image
on SD card...

  Boot the card -- copy your custom scripts from eMMC to equivalent
location on the SD card (you do have them in a nice isolated location,
don't you?). Reboot to confirm they are working. Then... if you don't want
to run off the SD card, convert the card to a flasher and flash the
contents back to the eMMC -- remove SD card, reboot, test.

Suggested image, and flasher instructions:

OK, thanks, that sounds pretty straightforward. Yes, my scripts are
in a well defined (and backed up off board) place.